V 

UC-NRLF 


C   3   550   Efli4 


W.    B.   No.  S7'2. 


U.  S.  DEPARTMENT  OF  AGEICULTURE, 

WEATHER    BUREAU. 


STUDIES  ON   THE   THERMODYNAMICS  OF   THE 


ATMOSPHERE 


Reprints  from  the  Monthly  Weather  Review,  January,  February,  March,  June,  July,  August,  October,  November, 

and  December,  1906. 


FRANK  HAGAR  BIGELOW,  M.  A.,  L.  H.  D., 

Professor  of  Meteorology. 


Prepared  under  the  direction  of  WILLIS   L.   MOORE,  Chief  U.  S.  Weather  Bureau. 


WASHINGTON: 

WEATHER     BUREAU. 
1907. 


W.  B.  No.  372. 


U.  S.  DEPARTMENT  OF  AGRICULTURE, 
WEATHER    BUREAU. 


STUDIES  ON   THE   THERMODYNAM 


ATMOSPHERE. 


Eeprints  from  the  Monthly  Weather  Review,  January,  February,  March,  June,  July,  August,  October,  November, 

and  December,  1906. 


BY 


FBANK  HAGAK  BIGELOW,  M.  A.,  L.  H.  D., 
//; 

Professor  of  Meteorology. 


Prepared  under  the  direction  of  WILLIS   L.   MOOKE,  Chief  U.  S.  Weather  Bureau. 


WASHINGTON: 

WEATHER     BOKEAU. 

1907. 


OOITTE1ITTS. 


I. —  Asymmetric  cyclones  and  anticyclones  in  Europe  and 
America 

Introductory  remarks 

The  supposed  difference  in  the  temperature  distribution  be- 
tween American  and  European  cyclones  and  anticyclones 

The  temperature-falls  at  Blue  Hill  and  Hald-Berlin 

Explanation  of  Tables  1,  2,  3,  and  4 

Temperature-falls  from  the  surface 

Temperature  differences  at  the  same  elevation 

Vertical  temperature  gradients  per  100  meters 

Vertical  temperature  gradients  in  the  warm  and  cold  areas 

Results 

II. —  Coordination  of  the  velocity,  temperature,  and  pressure  iu 
the  cyclones  and  anticyclones  of  Europe  and  North 
America 

The  adopted  mean  temperatures  and  gradients  on  the 
1000-meter  levels  for  American  and  European  cyclones 
and  anticyclones 

The  variations  of  temperature  in  the  several  sectors  of 
cyclones  and  anticyclones  on  each  1000-meter  level 

The  mean  temperature,  T,  in  cyclones  and  anticyclones. . . 

Resume  of  the  typical  distributions  of  the  velocity,  tem- 
perature, and  pressure  in  cyclones  and  anticyclones. . .  . 
III.— Application  of  the  thermodynamic  formula  to  the  nonadia- 
batic  atmosphere 

The  nonadiabatic  atmosphere 

Development  of  the  thermodynamic  formula 

I.  The  first  form  of  the  barometric  formula 

II.  The  second  form  of  the  barometric  formula  in  an 
adiabatic  atmosphere 

III.  The  barometric  formula  in  a  nonadiabatic  atmosphere 

IV.  Construction  of  the  primary  differential  equation. . .  . 
V.  Application  to  the  general  equations  of  motion 

VI.  Four  systems  of  constants  for  the  atmosphere 

VII.  The  thermodynamic  constants  for  the  sun 

IV. — Numerical  computations  in  the  vertical  ordinate 

Three  general  theories  regarding  the  formation  of  cyclones 
and  anticyclones 

Comparison  of  the  numerical  results  of  computations  by 
formula  (38)  and  the  general  barometric  formula  of  the 
cloud  report  (59) 

Computation  of  mean  values  of  P0,  />„,  Ra,  from  T0  on  the 
1000-meter  levels 

Collection  of  the  data  showing  the  distribution  of  the  dis- 
turbances on  the  1000-meter  levels 

Values  of  the  temperatures  T,  T0,  and  T—  ro 

Values  of  the  ratios  n,  na  and  (n — n0) 

Values  of  the  terms  Cp  n  (T—  T0)  and  (2-  zc) 

Distributions  of  the  velocities  q,  qa  \  (if—  qj) 

The  distribution  of  the  heat  Q—  §„ 

Distribution  of  the  pressure  B—B0 

V. — The  horizontal  convection  in  cyclones  and  anticyclones  . . 

Some  of  the  difficulties  in  this  problem 

The  horizontal  circulation 

The  horizontal  pressure  gradients 

The  horizontal  interchange  of  heat  energy 

Some  cases  of  restricted  conditions 

General  thermodynamic  equations 

Case  I.  Change  of  position  in  the  layers  in  a  column  of  air 

Case  II.  The  temperature  is  a  continuous  function  of  the 
height,  T!=Tl  —  ah 

Case  III.  For  local  changes  between  two  adjacent  strata 
of  different  temperatures,  where  on  the  boundary  the 
pressure  P=P',  =  .P'2,  and  the  temperature  is  discon- 
tinuous  

Case  IV.  The  overturn  of  deep  strata  in  the  column 

Case  V.  Transformation  of  two  masses  of  different  temper- 
atures on  the  same  level  into  a  state  of  equilibrium .... 

Case  VI.  Continuous  horizontal  temperature  distribution 
with  adiabatic  vertical  gradient 

Case  VII.  Position  of  layers  of  equal  entrophy  when  the 
pressure  at  a  given  level  is  constant  and  the  tempera- 
ture at  this  level  is  a  function  of  the  horizontal  distance 
and  a  linear  function  of  the  height 


9 

9 

9 
10 
11 
12 
14 
14 
15 
16 


74 


74 

75 
77 

77 

110 

110 

111 

111 

111 

112 
113 
114 
115 
116 
265 

265 


265 
265 

267 
267 
267 
270 
271 
271 
271 
562 
562 
563 
564 
563 
566 
567 
568 

568 


569 
570 

570 

571 

571 


Page. 

Case  VIII.  Final  condition  of  two  air  masses  under  con- 
stant pressure  with  given  initial  linear  vertical  tem- 
perature fall 571 

VI. — The  waterspout  seen  off  Cottage  City,  Mass.,  in  Vineyard 

Sound,  on  August  19,  1896 307 

The  sources  of  the  data  used  in  the  discussion 307 

Letters  and  reports  of  observers 307 

The  photographs 313 

Position  of  the  waterspout  in  the  Sound 314 

Dimensions  as  measured  on  photograph  2d  A,  fig.  27   314 

VII. — The  meteorological  conditions  associated  with  the  Cottage 

City  waterspout 360 

Meteorological  conditions  for  August,  19,  1896 360 

Probable  conditions  near  the  waterspout 360 

Computation  of  the  pressure  B,  temperature  t,  vapor  ten- 
sion e,  and  height  H,  for  the  n,  /3,  y,  6  stages 362 

(A)  The  o-stage,  or  unsaturated  process 363 

(B)  The  /3-stage,  or  saturated  process 365 

(C)  The  >  -stage,  or  freezing  process 366 

(D)  The  rf-stage,  or  frozen  process 366 

The  cause  of  the  formation  of  the  waterspout  cloud,  and 

the  vertical  convectional  velocity 369 

VIII. — The  meteorological  conditions  associated  with  the  Cottage 

City  waterspout— continued 470 

Relations  between  wind  velocities  and  atmospheric  pres- 
sures    470 

Marvin's  correction  to  observed  wind  velocities 476 

IX. — The  meteorological  conditions  associated  with  the  Cottage 

City  waterspout— continued 511 

The  maximum  falling  velocity  for  rain  in  the  lower  atmos- 
phere    511 

The  probable  vertical  velocity  in  the  cloud 512 

Approximate  position  of  the  isotherms  and  isobars  in  the 

Cottage  City  waterspout  cloud 513 

The  building  of  hail : 514 

Theories  of  the  formation  of  hailstones 515 

TABLES. 

Table    1.— Temperature-falls  at  Blue  Hill 10 

High  areas  in  winter 10 

Low  areas  in  winter 10 

2.— Temperature-falls  at  Blue  Hill 11 

High  areas  in  summer 11 

Low  areas  in  summer 11 

3. — Temperature-falls  at  Hald  and  Berlin  12 

High  areas  in  winter    12 

Low  areas  in  winter 12 

4. — Temperature-falls  at  Hald  and  Berlin 13 

High  areas  in  summer 13 

Low  areas  in  summer 13 

5. — Surface  temperatures  in  centigrade  degrees  for  day  and 

night  at  Hald  and  Berlin 14 

High  areas 14 

Low  areas 14 

6. — Distribution  of  the  sectors  by  warm  and  cold  areas. ...  14 
7. — Temperatures  and  gradients  in  the  American  and  Euro- 
pean cyclones  and    anticyclones    arranged   by    the 

warm  and  cold  areas 15 

8. — Temperature  differences,  cold  minus  warm  areas 15 

9. — Temperatures  and  variation  of  temperature  on  each 
1000-meter  level  in  American  cyclones  and  anti- 
cyclones    74 

American  winter  high  areas 74 

American  winter  low  areas 74 

American  summer  high  areas 74 

American  summer  low  areas 74 

10. — Temperatures  and  variation  of  temperature  on  each 
1000-meter  level  in  European  cyclones  and  anti- 
cyclones    '  75 

European  winter  high  areas 75 

European  winter  low  areas 75 

European  summer  high  areas ; .  75 

European  summer  low  areas 75 

iii 


IV 


Page. 

Table  11. — Adopted  mean  temperatures  and  gradients  on  the  1000- 
meter  levels  for  American  and  European  cyclones  and 

anticyclones 75 

12. — Adopted   mean    temperature    variations,     —  AT,    in 

American  and  European  cyclones  and  anticyclones. .  76 

Winter 76 

Summer 76 

13. — Mean  temperature,  T,  in  cyclones  and  anticyclones.    .  77 

Winter 77 

Summer 77 

14.— Mechanical  systems  of  consonants  for  the  atmosphere 

in  gravitational  units 115 

15.— Comparison  of  the  formulae 266 

16.— Computed  values  of  the  ratio,  n,  between  successive 

1000-meter  levels 266 

17. — Computed  mean  values  of  pressure,  density,  and  gas 
factor  from  the  temperature  at  several  elevations, 

European  winter 207 

18.— European  summer 267 

19. — American  winter 267 

20.  — American  summer 207 

21.— Values  of   T,   Ta,   T-  '!'„  derived   from  Tables  12,  13, 

winter  high  areas 268 

22.— Winter  low  areas 268 

23.— Summer  high  areas '. 268 

24. — Summer  low  areas 268 

25. — Distribution  of  the  values  of  n,  nc,  n  -  n0,  winter  high 

areas 268 

26.— Winter  low  areas 268 

27. — Summer  high  areas. .  . . ; 268 

28. — Summer  low  areas 268 

29. — Distribution  of   the   heights  z— z0.  (z— za)  g=  -  t    na, 

(T—  T0),  winter  high  areas 269 

30.— Winter  low  areas 269 

31.—  Summer  high  areas 269 

32.—  Summer  low  areas 269 

33. — Distribution  of  the  velocities  q,  qa,  4  (</*  —  g20),  winter 

high  areas ". 269 

34.-  Winter  low  areas 269 

35.— Summer  high  areas 269 

36.  -  Summer  low  areas 269 

37. — Distribution  of  the   heat,   y  —  Qa,  and   the  pressure, 

B—  B0.,  winter  high  areas 270 

38.— Winter  low  areas: 270 

39. — Summer  high  areas 270 

40. — Summer  low  areas 270 

41. — Vertical  displacement,  z —  s0,  from  equilibrium 563 

42. — Computation  of  the  pressure  B  in  the  cold  and  warm 

maxima  on  each  1000-meter  level 565 

43.— I.  Mean  values  of  the  gradient  ratio  n  in  the  cold  and 

warm  maxima 565 

II.  Mean  values  of  the  temperature  T  in  the  cold  and 

warm  maxima 565 

III.  Mean  values  of  the  velocity  term  in  the  cold  and 

warm  maxima. 505 

44. — Values  of  the  terms  in  the  formula 566 

Tables  45  to  49,  inclusive,  have  been  omitted  from  pub- 
lication. 

50.— (A)  Meteorological  data  for  August  19,  1896 362 

(B)  Kecords  for  ten  days  either  side  of  August,  19,  1896 .  302 

(C)  Continuous  self-register  of  pressure  and  tempera- 

ture at  Nantuckett,  Mass.,  August  19,  1896 362 

51. — Summary  of  the  data  for  the  Cottage  City  waterspout, 

August  19,  1896 368 

52. — Formulas  for  wind  velocities  and  pressure  gradients  .  .  470 
53. — Barometric  gradient  sustaining  an  eastward  velocity 

only 470 

54. — The  Newtonian  theorem 471 

55. — The  vertical  velocity  that  just  sustains  a  freely  falling 

body 471 

56.— Velocities 472 

57.— Conversion  factors  for  units  of  length,  mass,  and  pres- 
sure    472 

58. — Conversion  factors  for  units  of  distance,  time,  and 

velocity 473 

59. — Conversion  factors  for  pressures  and  velocities 473 

60. — Resistance  to  a  solid  moving  in  a  fluid 473 

61. — Differential  coefficients 473 

62.  —Coefficient  for  viscosity  for  air,  p 474 

63. — Percentage  of    front  and  back  pressure  (Irminger's 

results) 476 

64.— Corrected  wind  velocities  as  indicated  by  a  Robinson 

anemometer,  in  miles  per  hour 476 

65. — Probable  sustaining   vertical    velocities,  w,  for   hail- 
stones    478 


Table  00.— I.  For  fine  drops,  0.01  to  0.02  mm 

II.  For  common  drops,  0.30  to  0.50  mm 

III.  For  large  drops,  1.00  to  5.50  mm 

07.—  Computation  of  the  isobars  at  three  hours,  August  19, 
1896.. 


Page. 
511 
511 
511 

514 


ILLUSTRATIONS. 

Figure    1. — American  and  European  temperature-falls  A  T,  in  high 

and  low  areas,  in  winter  and  summer 

2. — American  and   European  temperature-falls,    A   T,  in 

\v;irm  and  cold  areas,  in  winter  and  summer 

3. — The  distribution  of  temperature  in  the  high  and   low 

pressure  areas  of  North  America 

4. — The  distribution  of  temperature  in  the  high  and  low 

pressure  areas  of  Europe 

5. — Mean  temperature   variations,  A  T,  in  American  and 

European  cyclones  and  anticyclones 

6. — Mean   temperature   distribution,   T,  in  cyclones  and 

anticyclones 

7. — Adopted  temperature  distribution,  derived   from   the 

mean  American  and  European  observations 

8.— Temperature-fall  per  1000  meters  in  each  quadrant.  .  . 
U.  —  Typical  distribution  of  the  velocity,  temperature,  and 

pressure  in  cyclones  and  anticyclones 

10. — Typical  distributions  of  the  cyclonic  and   anticyclonic 

components  of  velocity,  temperature,  and  pressure. 

11. — Probable  arrangement  of  isothermal  surfaces.  ...;... 

12.  — The  relation  of  the  observed  to  the  adiabutic  gradient 

d  T. 


13. — The  variations  of  the  ratio  n  = 
14 


dT 


15.— 

10.- 
17.- 
18.- 
19.- 


20.- 
21.- 
22.— 

23.- 


24, 

21. 
24 

•24. 
21. 
•25. 


Distribution  of  the  values  n  —  ra0  in  the  high  and  low 
areas 

Distribution  of  z  —  z0  =  —  C  ""  (T  —  T0). . 

9 

Distribution  of  the  velocity  term  i  (</'  —  </„') 

Distribution  of  the  heat  Q—  QQ  . ." 

Distribution  of  the  pressure  B  —  Ba 

Scheme  of  the  transformation  of  adiabatic  gradients 
into  observed  temperature  gradients  thru  the  heat 
terms  (Q  —  Qa)  and  the  velocity  terms  [(</* —  </02)] . 

The  conversion  of  vertical  falls  into  horizontal  circula- 
tion   

Scheme  of  the  horizontal  circulation  in  cyclones  and 
anticyclones 

Illustrating  the  relation  of  the  thermodynamie  gra- 
dients to  the  hydrodyuamie  pressures  in  cyclones 
and  anticyclones 

Mean  values  of  the  gradient  ratio,  n,  at  the  cold  and 
warm  maxima 

A 

B  

C 

D 


-E 


Location  of  waterspout  seen  in  Vineyard  Sound,  Au- 
gust 19,  1896  

26. — Diagram  of  the  survey  between  the  site  of  Chamber- 
lain's camera  and  four  telegraph  poles  shown  in  his 
photograph,  2d  A  (flg.  27) 

27.— 2d  A;  second  appearance;  Chamberlain;  Cottage  fit  v, 
1:02  p.  m 

28. —  2d  15;  second  appearance;  Coolidge;  Cottage  City; 
1 :03  p.  m 

29. — 2d  C;  second  appearance;  Hallet;  Cottage  City;  1:08 
p.  m 

30. — 2d  D;  second  appearance;  Dodge;  Vineyard  Haven; 
1 :12  p.  m 

31. — 2d  E;  second  appearance;  Ward;  Falmouth  Heights; 
1 :14  p.  in 

32.— 2d  F;  second  appearance;  Coolidge;  Cottage  City; 
1:15  p.  m 

33.— 2d  G;  second  appearance;  Coolidge;  Cottage  City; 
1:17  p.  m 

34.— 3d  A;  third  appearance;  Chamberlain;  Cottage  City; 
1 :20  p.  m 

35. — 3d  B;  third  appearance;  Chamberlain;  Cottage  City; 
1 :24  p.  m 

36. — 3d  C;  third  appearance;  Coolidge;  Cottage  City;  1:27 
p.  m '. 

37. — Weather  conditions,  Wednesday,  August  19,  1896,  at 
8  a.m.,  75th  meridian  time,  preceding  the  water- 
spout   

38. — Special  form  of  whirling  apparatus  used  by  Dines. . .  . 

39. — Approximate  position  of  isotherms  and  isobars 

40.  — Stratification  of  /)-  and  <!-stage  in  a  cloud  with  hail 


12 
12 
12 

12 

77 
77 

77 
76 

77 

77 
110 
112 

113 

271 
271 

271 
271 
271 

271 
563 
564 

564 

566 
508 
570 
570 
571 
571 

308 

309 
314 
314 
314 
314 
314 
314 
314 
314 
314 
314 


361 
475 
513 
517 


JANUARY,  1906. 


MONTHLY  WEATHEE  REVIEW. 


9 


From  the  right  spherical  triangle  PBE,  figs.  2  and  3,  we 
have — 

(1)  Cos  ft  =  cos  a  cos  ft. 

(2)  Cot  H.  A.  =  cot  a  sin  ft. 

Let  a  and  ft  be  two  variables  in  Cartesian  rectangular  co- 
ordinates. Assign  ft  a  constant  value  and  let  a.  and  ft  vary; 
then  from  the  first  of  these  equations  a  certain  definite  curve 
will  be  traced  as  shown  in  the  diagram  (see  fig.  4),  and  by 
assigning  arbitrary  values  to  ft,  from  0°  up  to  90°,  a  family  of 
declination  curves  will  be  obtained.  In  the  same  manner 
there  will  result  a  family  of  hour  angle  curves  (see  fig.  5)  by 
assigning  arbitrary  values  to  the  hour  angle  H.  A.,  and  then 
letting  «  and  ft  vary.  By  constructing  the  two  series  of  curves 
on  the  same  set  of  coordinate  axes  these  results  follow. 

Thus  the  plane  area  is  divided  into  a  series  of  curve  line 
quadrilaterals  which  may  be  made  as  small  as  we  please  by 
tracing  the  curves  at  sufficiently  small  intervals. 

If  one  value  of  '5  and  one  of  H.  A.  be  given,  then  by  means 
of  these  curves  the  position  of  a  point  is  fixed  in  the  plane. 
The  rectangular  coordinates  of  this  point  are  the  values  of  a 
and  ft  corresponding  to  these  values  of  ft  and  H.  A.  Conversely, 
if  we  know  the  values  of  «  and  ft,  we  are  enabled  to  plot  the 
position  in  the  plane,  and  we  can  read  off  ft  and  H..A.  by  means 
of  the  curves. 

By  means  of  this  abacus,  the  azimuth  and  altitude  of  a  star 
may  be  determined  when  its  declination  and  hour  angle  and 
the  estimated  colatitude  are  given.  Plot  the  position  of  the 
star  by  means  of  ft  and  H.  A.  curves,  estimating  the  minutes  by 
the  eye,  and  read  the  rectangular  coordinates  of  the  point 
thus  plotted,  n  on  the  vertical  scale  and  ft  on  the  horizontal 
scale.  The  H.  A.  curves  here  represent  meridians  and  the  ft 
curves  represent  parallels  of  the  celestial  sphere.  Now  make 
K  =  ).  +  ft,  considering  ft  negative  if  the  latitude  and  decli- 
nation are  of  contrary  name.  Plot  the  point  which  has  a  and 
B  for  rectangular  coordinates,  and,  considering  now  the  H.  A. 
curves  to  represent  verticals,  and  the  3  curves  to  represent  cir- 
cles of  equal  latitude,  read  off  the  azimuth  by  means  of  the 
H.  A.  curves,  and  the  altitude  due  to  the  estimated  latitude  by 
means  of  the  '5  curves. 

This  abacus  will  also  serve  to  find: 

(1)  The  time  of  rising  and  setting  of  a  star  and  its  azimuth 
in  the  horizon. 

(2)  The  name  of  an  observed  star. 

(3)  The  distance  and  great  circle  course  between  two  points. 

Through  the  initiative  of  Monsieur  Eugene  Pereire,  Presi- 
dent of  the  Administrative  Council  of  the  Compagnie  Generale 
Transatlantique,  this  method  has  been  published  in  rectangu- 
lar coordinates  on  four  grand-eagle  pages  on  a  scale  of  T 

of  a  meter  to  the  degree,  and  may  be  purchased  in  France. 


STUDIES  ON  THE  THERMODYNAMICS  OF  THE  ATMOS- 
PHERE. 

By  Prof.  FRANK  II.  BIGELOW. 

I.— ASYMMETRIC   CYCLONES   AND   ANTICYCLONES  IN   EUROPE 
AND  AMERICA. 

INTRODUCTORY  REMARKS. 

The  synthetic  construction  of  the  correct  statement  of  the 
mechanical  problems  involved  in  the  cyclonic  and  anticyclonic 
circulations  of  the  atmosphere  depends  upon  the  coordination 
of  the  data  derived  from  observations  of  the  velocity  vectors, 
the  pressures,  and  the  temperatures  prevailing  in  the  moving 
air  masses.  In  my  International  Cloud  Report,  1898,  and  in 
the  MONTHLY  WEATHER  REVIEWS  for  January,  February,  and 
March,  1902,  the  distribution  of  the  velocity  vectors  for  the 
United  States  was  described;  in  the  REVIEWS  for  January  and 
February,  1903,  the  distribution  of  the  pressures  correspond- 
ing to  these  velocities  was  explained;  in  this  present  series 
of  papers  the  results  of  my  studies  on  the  relation  of  the  tem- 
2 2 


peratures  to  the  velocities  and  pressures  will  be  summarized. 
It  has  been  shown  conclusively  for  the  United  States  that 
there  are  no  true  local  warm-centered  and  cold-centered 
cyclones  or  anticyclones  in  the  atmosphere,  and  that  all  the 
theoretical  discussions  or  theses  founded  on  that  basis  are 
misdirected.  The  observations  demonstrate  that  in  the  lower 
atmosphere  the  actual  mechanism  consists  of  rather  deep  warm 
and  cold  countercurrents  of  air,  which  underrun  the  pre- 
vailing eastward  drift.  The  centers  of  gyration  are  uniformly 
in  the  region  where  these  counterflowing  currents  meet  each 
other,  that  is  to  say,  on  the  edges  rather  than  in  the  midst  of 
the  warm  and  cold  regions.  About  one  half  of  the  cyclone  is 
relatively  warm  and  the  other  half  cold,  while  the  opposite 
half  of  the  anticyclone  is  warm  and  its  alternate  half  is  cold. 
Thus,  in  the  United  States,  the  eastern  and  northern  sectors 
of  the  cyclone  with  the  western  and  northern  sectors  of  the 
anticyclone  are  warm,  while  the  western  and  southern  sectors 
of  the  cyclone  and  the  eastern  and  southern  sectors  of  the 
anticyclone  are  cold.  The  warm  air  flowing  from  the  south- 
west into  the  east  of  the  cyclone  and  west  of  the  anticyclone, 
and  the  cold  air  flowing  from  the  northwest  into  the  east  of 
the  anticyclone  and  the  west  of  the  cyclone,  constitute  two 
currents  whose  temperatures  differ  from  each  other  and  from 
the  normal  temperature  of  the  prevailing  eastward  drift. 
These  currents  seek  to  equalize  their  different  temperatures 
by  interpenetration,  and  in  so  doing  the  circulating  structures 
known  as  cyclonic  and  anticyclonic  are  established.  The  heat 
added  to  the  tropical  zones  of  the  earth  by  the  solar  radiation 
is  to  a  considerable  extent  transported  into  the  temperate 
zones  by  long  horizontal  currents  in  the  lower  levels,  and  is 
there  expended  in  generating  local  circulations.  These  pene- 
trate the  upper  current  of  eastward  drift  and  tend  to  retard 
its  motion,  slowing  it  down  to  the  moderate  velocities 
which  have  been  found  to  exist  within  ten  miles  of  the  ground. 
This  stratification  and  interpenetration  of  currents  of  different 
temperatures  is  the  true  source  of  the  energy  of  storms.  The 
heat  energy  derived  from  the  condensation  of  aqueous  vapor 
to  water,  and  the  energy  produced  by  purely  dynamic  eddies 
are  entirely  secondary  in  importance  to  the  thermodynamic 
energy  obtained  by  the  counterflow  and  underflow  of  warm 
southerly  currents  against  the  cold  northerly  currents  and 
beneath  the  eastward  flowing  drift.  In  the  present  series  of 
papers  it  is  purposed  to  examine  somewhat  fully  the  thermo- 
dynamic conditions  which  exist  in  the  atmosphere,  especially 
in  cyclones,  anticyclones  and  tornadoes;  at  present  the  tem- 
perature data  are  inadequate  for  a  satisfactory  consideration 
of  hurricanes  and  the  general  circulation,  though  something 
may  also  be  done  in  that  direction. 

THE     SUPPOSED     DIFFERENCE     IN    THE    TEMPERATURE     DISTRIBUTION    BE- 
TWEEN   AMERICAN    AND    EUROPEAN    CYCLONES    AND    ANTICYCLONES. 

Certain  discussions  of  the  available  temperature  observa- 
tions made  at  different  levels  in  cyclones  and  anticyclones  for 
the  United  States  and  Europe  indicate  that  there  is  a  serious 
disagreement  in  the  results  for  the  respective  regions,  as 
if  these  local  circulations  might  really  be  different  in  some 
important  respects.  We  should  not  expect  to  find  any  such 
divergence  in  the  thermodynamics  of  the  atmosphere  when 
the  observations  and  the  computations  have  been  accurately 
made,  but  as  it  is  comparatively  difficult  to  extract  the  exact 
truth  of  the  matter  from  the  actual  observations,  it  will  be 
proper  to  examine  these  observations  carefully  before  admit- 
ting that  any  important  difference  in  the  structures  actually 
exists.  A  suitable  review  of  the  literature  may  be  found  in 
Mr.  Clayton's  article,1  from  which  the  following  few  statements 
are  compiled: 

From  a  study  of  mountain  observations.Professor  Hann  found 

1  Various  researches  on  the  temperatures  In  cyclones  and  anticyclones 
in  temperate  latitudes.  By  H.  Helm  Clayton.  Beitrage  zur  Physik  der 
frelen  Atmosphare.  Vol.  I,  pp.  93-106. 


10 


MONTHLY  WEATHER  REVIEW. 


JANUARY,  1906 


TABLE  I.— Temperature-falls  at  Blue  Hill. 

HIGH  AREAS  IN  WINTER  (OCTOBER  TO  MARCH). 


Height 

North  (8). 

East  (9). 

South  (10). 

West  (3). 

Mean. 

meters. 

F       No.     AT          T 

F       No.    AT           T 

F       No.     AT           T 

F       No.    AT          T 

r       — 

100 

4000 

°  F.              °F.       °C. 
21  2          79 

Of                        Of.             0  (J 

_37  4    —18.8 

Of                        Of             0C 

—31.0    —17.9 

°F.          °  F.       °C. 
29  8          76 

°c.      °a 

13  1     —0  50 

'•Mill 

10  6      1        19  8         73 

36  1      2    —  35  2        17  6 

.     —28  9        16  8 

28  0          66 

12  1     —  0  55 

3600 

18  7      3        18  2         64 

82  0      2    —S3  2     —16.  3 

—27  0    -15.7 

—26  6          68 

11  1     —  0  50 

MOQ 

17  B      2        16  8          5.6 

—32.8      3    —30.9    —15.1 

—20.5      1     —25.0    —14.6 

—25.  2     —  5  0 

—10.1     —0.60 

8200 

13  9      2        16  2          47 

27  9      4        28  7    —14.0 

—20.  6       1     —23.  1     —13  6 

23  8    —  4  2 

91     —  0  50 

3000 

13  7      2        13  7         3.9 

—32.1      5    —26.8    —12.7 

—17.8      2    —21.3    —12.6 

—21.8    —  8.1 

—  8  1    —  0.48 

2800 

12  5      3        12.2         81 

23  6      8        24  5        11  6 

19  2      3    —19.8        11  7 

20  5          24 

72        0  40 

•V.IHI 

-    10  2      3        11  0          24 

—15  0      5     —22.3    —10  4 

—  18.4    —10  9 

12  7       1         19  0    —  1  6 

64        0  40 

2400 
2200 
2000 

-10.1       3    —10.2    —2.0 
—  6.4      1    —9.4    -  1.8 
695         88         12 

-20.  8      1    —20.  4    -  9.  8 
—16.3      6    -18.8    —8.3 
18  3      7        16  5    —  71 

—16.7    —10.0 
—17.4      1     —15.8    —9.4 
+  65      1        13.  7         88 

—17.7      1    —17.7    —0.9 
-13.2      2    —16.1          0.0 
14  4          10 

—  5.6    -0.40 
—  4.8    —0.45 
39        0  60 

1800 

92      4         60         04 

12  5      6        14  7    —  6  2 

11  6    —  7  2 

17  6      1         12  4          21 

27        0  60 

10(11) 
1400 
1200 
1000 

800 
600 

KIM 

200 
0 

—  8.2      4    —  4.2         1.4 
+  0.2      1—8.0         2.0 
—  6.7      3    —  2.6         2.1 
+  0.8      2    —  3.6          1.8 

—  8.1      4    —4.6          1.1 
—  7.9      1    —4.4          1.3 
—  3.7      4    —3.6          1.7 
—  1.3    50    —  1.8         2.7 
88.7    50       38.7         3.7 

—16.8      4    —12.6    —  5.0 
—10.9    18    —11.8    —  4.3 
—12.0      8    —10.4    —  3.8 
—  8.0    11    —  9.8    —  8.6 

—  6.0    18    —8.7    —  2.8 
—  9.3    15    —  6.8    —  1.8 
—  4.1    16    —  4.3    —  0.4 
—  1.4  151     —  2.0         0.9 
35.6151         35.6          2.0 

+  2.3      6    —  9.4     —  5.9 
—  4.5      8    -  6.8    —  4.5 
—  5.8      6    —  5.3    —  3.7 
—  2.6      8    -5.2    -3.6 

—  «.6    13    —  5.8    —  3.9 
—  7.8    17    —  6.0    —  4.0 
—  5.0    16    —  5.2    —  8.6 
—  2.5  107    —  3.2    —  2.5 
30.7  107        30.7    —  0.7 

—12.0      2    —10.4         3.4 
—  8.5      3—9.2         8.9 
—  7.4      7—8.6         4.2 
—  7.6      8    —  8.2         4.5 

—  9.5      7    —  7.2         5.0 
—  6.4      6    —  6.0         6.7 
—  3.3      1     —  8.7          7.0 
—  2.1    36    —  2.0         7.9 
48.2    36        48.2         9.0 

—  1.5    -0.40 
-  0.7    -0.20 
-  0.3    —0.05 
—  0.2    —0.15 

0.1     —0.10 
0.3    —0.45 
1.2    -0.55 
2.3    —0.60 
3.5 

Mean  -0.  42 

LOW  AREAS  IN  WINTER. 


Height 

North  (0). 

East  (6). 

South  (13). 

West  (7). 

Mean. 

meters. 

F       No.     AT           T 

F       No.     AT          T 

F       No.     AT           T 

F       No.     AT          T 

r       Ar 
too 

4000 

Of                        Of             0  ff 

of              of.       o£ 
.  .     .  .     —28.  7    —13.  2 

°F.             °  F.         °C. 
-45  0        18  7 

Of                  Of             Op 

—  24  0    —16  0 

0  a      °a 

16  0    —0  66 

—26  7         12  0 

43  0        17  6 

22  4        15  1 

14  9       0  45 

3600 

.     —25  2    —11.2 

40  8        16  4 

20  9    —14  3 

14  o    —0  50 

3400 

23.4    —10.2 

—38.7    —15.2 

—19.4    —13.5 

—13  0        0.55 

8200 

21.4    —  9.1 

—37  92        36  4        13  9 

18  0        12.7 

11  9        0  66 

3000 

—19.  7         8.  1 

—35.2      2        34  0    —12.6 

—  4.9       1     —16.0    —11.6 

10  8    —0.  56 

2800 

.     —17.8    —  7.1 

—31.1      2        32  0    —11  5 

—  3.  2      3    —14.  2    —10.  6 

9.7    —  0  50 

2600 

15  8    —  6  0 

30  1      3        29  6        10  2 

+  11      3        12  8         98 

87        0  60 

2400 

..     —14.0    —  5.0 

—26  54        27  0         87 

+  35      2    —11.2    —8.9 

7  5    —  0  48 

2200 

—10.9      3    —12.0    —  3.9 

—23.3      6     —24.8    —  7.5 

—  9.6      4     —10.0    —8.3 

—  6.6    —0.45 

2000 

—  8  3      6    —10.3    —  3.0 

—23  96        22.7          6.3 

4.  5      5    —  9.  2          7.  8 

6.7    —  0  40 

1800 

6.  5      8    —  9.  2    —  23 

—20.  25        20  3         6.  0 

—10.7      7     —8.5     —7.4 

—  49    —  0  20 

1600 

' 

—10.7      3    —9.3    —  2.4 

—18.0    20    —18.0    —  3.7 

-  9.6      5    —  8.4    —7.3 

—  4.  5        0.  16 

1400 

86      7         9.  8    —  2.  7 

—15  7    23        16  0         2.6 

72      7          8.  4    —  7.  3 

—  4  2        0  25 

1200 

—10.2      8    —10.0    —2.8 

—14.0    31    —13.8    —  1.4 

—  8.  2      8     —  7.  9     -  7.  0 

—  3.  7        0.  25 

1000 

10  0      8         9.  8    —  27 

—10  3    22        11  4         01 

_96      8—  7.  3—  6.  8 

32        0  40 

800 

11  1      4         89          2.2 

8  2    17          92          12 

48      7         6.  1—  61 

2  4    —0  40 

600 

65      8    —  7.5    —  1.4 

—  8.  0    21    —  7.  3         2.  2 

—  5.6    11    —  5.0    —5.5 

—  1.6    —0.68 

400 

57      8—59         0.5 

—  41     13         47         37 

4  0    13         3.  7         4.  7 

0  5    —0  65 

200 

2  2    62    —  3.0          1.1 

—  1.6  185    —  24         50 

—  1.9109    —  2.  0    —  3.  8 

0.  8    —  0.  65 

0 

37.1    62        37.1          2.8 

43.4  185        43.3         6.3 

27.1  123        27.1    —2.7 

2.1        

Mean  —0.  43 

that  in  the  higher  levels  the  temperature  is  relatively  low  over 
cyclones,  but  high  over  anticyclones,  and  thence  he  supposed 
that  this  apparent  inversion  must  be  due  to  dynamic  actions, 
as  of  eddies  or  driven  whirls  in  the  prevailing  eastward  drift. 
To  somewhat  the  same  effect  the  investigations  of  Dechevrens, 
Berson,  and  Teisserenc  de  Bort  have  come,  namely,  that  "  cy- 
clones average  colder  than  anticyclones  below  nine  kilometers." 
On  the  other  hand,  the  investigations  of  Harrington,  Rotch, 
Hazen,  Clayton,  Shaw,  and  Dines  lead  to  the  conclusion  that 
"cyclones  average  warmer  than  anticyclones." 

The  discussion  of  the  temperatures  over  Hald  and  Berlin 
by  Grenander1  is  said  to  support  Hann's  proposition  rather 
than  the  American  view.  It  is  worth  while  to  find  whether 
this  contradiction  can  be  readily  reconciled.  Without  exam- 
ining critically  the  observations  themselves  and  the  methods 
of  reduction  that  have  been  employed,  it  is  sufficient  to  remark 
that  a  very  large  number  of  observations  is  required  to  arrive 
at  definitive  results,  and  that  both  the  annual  and  the  diurnal 
variations  of  temperature  must  be  eliminated  from  the 

*  Les  gradients  verticaux  de  la  temperature  dans  les  minima  et  les 
maxima  barom^triques.  Par  S.  Grenander.  Arkiv  f5r  matematik,  as- 
tronoml  och  fygik.  Bd.  2,  No.  7.  (1905.) 


temperature-falls  from  the  surface.  Mountain  observations 
require  a  series  of  local  corrections  to  be  applied  to  re- 
duce them  to  free  air  measures  of  temperature,  and,  gener- 
ally, the  observations  must  be  distributed  quite  uniformly 
throughout  the  24  hours.  The  tendency  is  to  use  an  excess 
of  daytime  observations,  and  this  will  produce  one-sided  data 
in  the  strata  up  to  at  least  the  elevation  of  3000  meters.  In 
the  following  exposition  it  will  be  sufficient  to  employ  the  data 
contained  in  Grenander's  paper  and  in  the  Blue  Hill  paper,3 
which  have  already  been  used  in  my  discussion  of  the  diurnal 
periods  of  the  temperature.  We  shall  expect  to  show  that 
the  structures  of  the  American  and  European  cyclones  and 
anticyclones  are  practically  the  same,  except  possibly  in  the 
lower  strata,  within  2000  meters  of  the  surface. 

THE  TEMPERATURE-FALLS  AT  BLUE  HILL  AND  HALD-BERLIN. 

The  reader  is  referred  to  my  paper  on  "The  diurnal  periods 
of  the  temperature  "  *  for  a  description  of  the  method  employed 
in  discussing  the  Blue  Hill  kite  observations  of  1897-1902. 

8  Observations  at  the  Blue  Hill  Observatory,  1901-2,  and  appendix 
of  the  observations  with  kites,  1897-1902,  with  discussion  by  H.  Helm 
Clayton.  , 

4  Monthly  Weather  Eeview,  February,  1905. 


JANUARY,  190C. 


MONTHLY  WEATHER  REVIEW. 


11 


TABLE  2.—  Temperature-falls  at  Blue  Hill. 

HIGH  AEEAS  IN  SUMMER  (APRIL  TO  SEPTEMBER). 


Height 

Center  (1). 

East  (24). 

South  (12). 

West  (8). 

Mean. 

meters. 

F       No.       H.T         T 

f       No.       AT         r 

F       No.       AT         T 

F       No.       AT         I 

r          AT 
100 

4000 

Of                          0  f             0  £ 

37  4        2.9 

°  F.          o  F.     °  a 

•    48  3        1         15  2        84 

°  F.                °  F.        °  C. 
.  .  .     —  43.  3        9.  6 

°  F.                °  F.        °  C. 
41  2        18 

0  a      °  c. 

—  6  4      —  0  80 

3800 
3600 
3400 
3200 

—38.9        2     —35.0    —1.5 
—30.8        2    —32.6     —0.2 
-31.8        4    —30.2        1.1 
27  2        2    —28.2        2.3 

-40.0         1     —  12.1     —6.7 
—45.  2        1     —39.  1     —5.  1 
—33.2        1     —36.0    —3.3 
—33.  0    —  1.  6 

-40.0    —7.7 
—36.7    —5.9 
—33.0         1     —33.5     -4.1 
—30.7        2     —30.2    —2.3 

—35.0         1     —38.7     —3.4 
—35.2        1    —36.2    —2.0 
—32.8        2    —33.8    —0.7 
—31.7        2     —31.5        0.6 

—4.  8      -0.  75 
—3.  3      —0.  75 
—  1.  8      —0.  75 

—0.  3         0.  70 

3000 
2800 

—27.7        5     -25.4        3.6 
22  2        6    —23.3        4  9 

-32.6        7    —29.8        0.1 
22  6      10        27  3        15 

—26.1         1     —27.2    —0.6 
—  28.0        1     —24.6        0.8 

—29.0        2.0 
—26.  6        3.  3 

1.  1      —0.  75 
26          0  70 

2600 
2400 
2200 
2000 

1800 
1600 
1400 
1200 
1000 

800 
600 
400 
200 
0 

—21.6        6     —21.2        6.1 
-17.0        6    —19.4        7.1 
—16.0        5    —17.3        8.3 
—18.2        5    —15.4        9.4 

—14.9      11    —13.6,    10.2 
-11.4        8    —11.8      11.3 
—10.2      11    —10.0      12.3 
—  7.  1      13    —  8.  5      13.  2 
—  7.  1       16     —  7.  9      13.  6 

—  7.  9      17    —  7.  6       13.  7 
—  1.9      24    —  6.  1       14.  5 
—  4.  3      25    —  4.  3      15.  5 
—  1.1     178    —  2.0       16.8 
64  3    178        64.3      17  9 

—22.1         5    —24.5        3.1 
—17.5        6    —22.2        4.4 
—20.7        9    —19.9        5.7 
-18.0        9     -17.4        7.1 

—18.7      15    —15.2        8.3 
—15.3      16    —12.6        9.7 
—11.4      20    —10.2      11.0 
—  8.  3      28    —  7.  4      12.  5 
—  4.  7      35    —  6.  7      13.  0 

—  2.  2      88    —  6.  0      13.  4 
+  2.  6      46    —  4.  7      14.  1 
—  1.  9      46    —  2.  5      15.  3 
—  0.9    326    —  0.6      16.3 
62.  0    326        62.  0      16.  7 

—17.1        1    —22.0        2.8 
—15.5        2     -20.0        3.4 
—  7.7        3    —18.0        4.5 
—12.7        5    —15.9        5.8 

—15.2        6    —13.5        7.0 
-16.1        7    —11.2        8.8 
—  7.6      15—9.1        9.4 
—  6.  8      10    —  7.  2      10.  5 
-  5.7      17—6.0      11.2 

—  4.8      14—5.3      11.5 
—  5.4      19—5.2      11.6 
—  5.3      19—4.6      11.9 
—  2.  6     134    —  2.  8      12.  9 
58.  1    134        58.  1      14.  5 

—32.5        3    —24.4        4.6 
—29.1         5    —22.2        5.8 
—22.0        7     -20.0        7.0 
-18.6        8    —18.0        8.1 

—17.4        7    —16.0        9.2 
—14.3        8    —14.6      10.0 
-17.8        8    —13.5      10.6 
—16.8        9    —12.0      11.4 
—13.2      11    —10.7      12.1 

—  7.3      13—9.2      13.0 
—  7.  9      18    —  7.  8      13.  8 
—  8.  4      10    -  6.  2      14.  7 
—  2.9    119    —2.7       16.6 
64.6     119        64.6      18.1 

4.  0       —0.  60 
5.  2      -Or60 
6.  4       —0.  60 
7.  6      —  0.  60 

8.7      —0.55 
9.  8      —0.  55 
10.  8      —0.  60 
11.9      —0.30 
12.5      —0.20 

12.  9      —0.  30 
18.5      —0.45 
14.  4      —0.  60 
15.  7      —  0.  55 
16.8      

Mean   —0.62 

LOW  AREAS  IN  SUMMER. 


Height 

Center  (4). 

East  (5). 

South  (22). 

West  (7). 

Mean. 

meters. 

F       No.       AT         T 

F       No.       AT         T 

f       No.       AT         T 

F       No.       AT          T 

T         ^ 
100 

4000 

°  F.                °  F.        °  C. 
44.  0     —9.  8 

°F.               °F.       °C. 
38.  8        6.  0 

°f.                °  F.        °  C. 
—48.  2    —3.  6 

Of                         Of             0   £ 

46.5    —9.0 

0  C.         °  C. 
—7.  1      —  0.  60 

3800 

12  3        89 

36  1        4.6 

—  45  0        21 

.     .  .    —  44.8        8.0 

59          0  55 

3600 
3400 

—41.8        1     —40.4    —7.8 
—38.8    —7.0 

—38.8        2    —34.6    —3.6 
—31.3        1     —32.2    —2.3 

—35.6        1    —43.2    —0.8 
—37.9        5    —41.0        0.4 

—41.5        1    -^13.0    —6.0 
—38.8        2    —40.7    —5.7 

_4.  8      —0.  60 

—3.  6    —o.  55 

3200 
3000 

2800 
2600 
2400 
2200 
2000 

1800 
1600 
1400 
1200 
1000 

800 
600 
400 
200 
0 

—37.3        1     -37.0    -6.0 
-35.5        3    —35.0    -4.8 

—33.2        3     —33.2    —8.8 
—28.9        4    —31.0     -2.6 
—29.7        6    -28.6    —1.8 
—26.8        7    —26.0        0.2 
—23.7        7    —23.5        1.6 

—25.3        3    —20.7        3.1 
—16.0        3     —18.0        4.6 
-14.1         6     -15.7        5.9 
—13.6        5     —13.2        7.3 
-12.1        6    —11.0        8.5 

-  9.  7        3     -  9.  2        9.  5 
—  7.  4        5    —  6.  8      10.  8 
—  3.  4        8    —  4.  3       12.  2 
-  3.  4      73    —  2.  0      13.  5 
68.2      73        68.2      14.6 

-33.3        2     -30.5    —1.4 
—31.8        3    —28.6    —0.3 

—35.5        4    —26.8       0.7 
—29.1        2    —24.8        1.8 
—25.4        2    —23.2        2.7 
—21.5        3    —21.0        3.9 
—15.3        4    —19.4        4.8 

-15.4        4     —17.0        6.2 
—14.9        5    —15.1         7.2 
—17.6        5    -13.3        8.2 
—11.1        6     —11.6        9.1 
-  5.  6        8    —  9.  7       10.  2 

—10.1        8—7.8      11.3 
—  5.  7        8    -  5.  7      12.  5 
—  5.8      11    —3.5      13.6 
—  2.7      82-1.6      14.7 
60.1      82        60.1      15.6 

-42.0        6    —38.8        1.6 
—31.9      13    —36.1        3.1 

—35.2      11     -34.6        4.0 
—30.9      14    —32.7        5.1 
—31.2      17    —30.4        6.3 
-28.8       18     —28.2        7.5 
—25.9       18    —25.8        8.9 

—24.0      23    —23.4      10.2 
—20.4      18    —20.8      11.6 
—  IM.-2      25    —18.1      18.1 
—16.7      22    —15.6      14.5 
—14.2      25    —13.0      16.0 

-11.0      33    —10.5       17.3 
—  8.9      38—8.0      18.8 
—  5.  5      40    —  5.  3      20.  2 
—  2.  7    341     —  2.  7      21.  7 
73.7     341         73.7      23.2 

—35.5        4    —38.4    —4.4 
—39.0        3    —36.4    —3.3 

—28.6        6    —34.0    —2.0 
—26.3        4    —31.5    —0.6 
—24.7        9     —29.6        0.5 
—23.0      12     —27.2        1.8 
—26.7        9    —25.0        3.0 

—25.9      12    —23.2        4.0 
—20.6        9    —20.8        5.3 
-20.3      12    —18.2        6.8 
—18.8       11     —16.0        8.0 
—13.7       12    —14.6        8.8 

—12.9      10    —12.0      10.2 
—  5.  9      12    —  7.  8      12.  3 
—  3.0      11—4.0      14.7 
—  1.  6    138    —  2.  0      15.  8 
62.6    145        62.5      16.9 

—2.  5      -0.  60 
—1.  8      —0.  50 

—0.  8      —0.  60 
0.  9      -0.  60 
2.  1      —0.  65 
3.  4      —0.  60 
4.  6      —0.  68 

5.  9      —0.  65 
7.  2      —0.  65 
8.  5      —0.  60 
9.  7      —0.  55 
10.  8      —0.  65 

12.  1       -0.  75 
13.6      -0.80 
15.  2      —  0.  60 
16.  4      —0.  60 
17.6       

Mean   —0.63 

It  is  convenient  to  utilize  the  same  data  for  discussing  the  dis- 
tribution of  temperature  in  the  several  strata  of  cyclones  and 
anticyclones  up  to  the  height  of  about  4000  meters,  for  the 
sake  of  eliminating  the  diurnal  variation.  This  was  done  by 
taking  the  mean  values  of  the  temperatures  as  observed  at 
the  several  ascensions,  which  were  distributed  in  the  differ- 
ent hours  of  the  day.  While  the  distribution  among  the 
24  hours  is  not  completely  uniform,  it  is  probable  that  a 
fairly  satisfactory  elimination  of  the  diurnal  temperature  vari- 
tion  in  the  levels  from  the  surface  to  3000  meters  has  been 
accomplished  in  my  computations,  by  taking  the  average  daily 
values  as  they  exist  in  this  report  for  the  winter  months  (Octo- 
ber to  March)  and  the  summer  months  (April  to  September), 
thus  making  two  groups  for  the  five  years  of  observations. 
The  number  of  available  observations  is  not  nearly  great 
enough  to  give  definitive  mean  values,  but  the  results  here 
explained  probably  indicate  quite  sufficiently  the  typical  con- 
ditions that  require  to  be  known  as  the  basis  of  a  theoretical 
discussion  of  the  thermodynamics  of  storms. 

Table  1,  temperature-falls  at  Blue  Hill,  winter  high  areas 
and  low  areas,  and  Table  2,  summer  high  areas  and  low  areas, 
summarize  the  data.  The  temperature-falls  are  given  for  the 


N.  E.  S.  W.  sectors,  and  for  the  center  when  possible.  These 
sectors  group  the  data  according  to  my  subareas  as  follows: 
For  center  we  take  subareas  ( 1,  2,  3,  4),  for  north  (9, 10, 17, 18), 
east  (7,  8,  15,  16),  south  (5,  6,  13,  14),  west  (11,  12,  19,  20). 
The  areas  at  the  time  of  observation  at  Blue  Hill  were  located 
in  respect  to  these  subareas  by  studying  the  corresponding 
weather  maps  and  selecting  the  most  conspicuous  high  area 
or  low  area  for  the  center. 

EXPLANATION    OF    TABLES    1,    2,    3,    AND    4. 

The  first  column  of  Table  1  gives  the  height  in  meters,  the 
second,  F,  the  mean  temperature-falls  in  Fahrenheit  degrees,  as 
determined  by  the  number  of  observations  recorded  in  column 
three;  these  temperature-falls  were  plotted  on  diagrams  and 
average  curves  were  drawn  through  the  points,  from  which 
the  values  of  JT  found  in  column  four  were  scaled,  and  these 
should  represent  more  exact  values  than  can  be  obtained  from 
the  limited  number  of  observations  at  our  disposal.  At  the 
bottom  of  columns  F  and  J  T  is.  found  the  mean  surface  tem- 
perature, determined  by  the  numerous  readings  made  at  the 
Blue  Hill  valley  station.  In  column  five,  marked  T,  are  given 
the  corresponding  temperatures  themselves  in  centigrade  de- 
grees, being  transformed  from  the  Fahrenheit  degrees  re- 


12 


MONTHLY  WEATHER  REVIEW. 


JANUARY,  1906 


TABLE  3. —  Temperature-falls  at  Hald  and  Berlin. 

HIGH  AREAS  IN  WINTER  (OCTOBER  TO  MAY  15). 


Uelght 
in 
meters. 

North. 

Bub 

South. 

West. 

Mean. 

AT           T 

AT            T 

AT            T 

AT           T 

T           A7? 
100 

6000 
8800 
5600 
5400 
6200 
5000 

°C.        °  C. 
—31.6    -27.0 
-30.0    —25.4 
-28.3    —23.7 
—26.7    —22.1 
-28.6    —20.9 
—24.2    —19.6 

°C.         °C. 
—34.  0    —33.  2 
—32.6    -31.7 
—31.0    —30.2 
-28.7    —27.9 
—26.7     —25.9 
-24.8    —24.0 

°C.        °C. 
—25.  3    —24.  5 
—23.9    —23.1 
—22.7    —21.9 
-21.7    —20.9 
—20.3    —19.5 
—19.1     -18.8 

°C.        °C. 
—25.  7     —21.  6 
—24.4    —20.3 
-22.9    —18.8 
—21.4    —17.3 
—19.8    —15.7 
—18.6     -14.6 

0  C.        °C. 
—26.6    —0.76 
—25.1     -0.70 
—23.7    —0.80 
—22.1     —0.80 
—20.  5    —0.  70 
—19.1     —0.60 

4800 
4600 
4400 
4200 
4000 

-22.8    -18.2 
—21.6    —17.0 
—19.8    —15.2 
—18.6    —14.0 
—17.8    —12.9 

—23.6    —22.8 
—22.4    —21.6 
—21.0    —20.2 
—20.0    -19.2 
-18.8    —18.0 

-18.1    —17.8 
—17.1     —16.3 
-15.7    —14.9 
—14.7    —13.9 
—18.7    —12.9 

—17.8    —13.4 
—16.3     —12.2 
-15.0    —10.9 
—14.0     -   9.9 
-12.6    —  8.5 

—17.9     -0.65 
—16.8    —0.76 
—15.3    -0.65 
—14.0    -0.45 
—13.1    -0.50 

3800 
3600 
8400 
3200 
3000 

-16.4     -11.8 
—15.4    —10.8 
—14.3    —  9.7 
—13.2    —  8.6 
-12.2    —  7.6 

—18.0    —17.2 
—17.2    -16.4 
—16.4    —15.6 
—15.1     —14.3 
—14.0    —13.2 

—12.8    —12.0 
—11.9    —11.1 
—10.9    —10.1 
—  9.8    —  9.0 
—  8.7    —  7.9 

—11.6    —  7.5 
—10.6    —  6.5 
—  9.6    —  5.4 
—  8.6    —  4.6 
—  7.4    —  3.3 

—12.1     —0.45 
—11.2    —0.50 
—10.2    —0.55 
—  9.1     —0.55 
—  8.0    -0.40 

2800 
2600 
2400 
2200 
2000 

—11.2    —  6.6 
—10.3    —  6.7 
—  9.4    —  4.8 
—  8.1    —  3.6 
-  7.1    —2.5 

—13.1    —12.3 
—12.3    —11.5 
—11.4    —10.6 
—10.7    —  9.9 
—  9.8    —9.0 

—  8.4    —  7.6 
—  7.8    —  7.0 
-  7.2    —  6.4 
—  6.7    —  6.9 
-  6.2    -  5.4 

—  6.9    —  2.8 
—  6.3    -  2.2 
-  5.4    —  1.3 
—  4.4    —  0.8 
-  3.6         0.5 

-  7.2    —0.40 
—  6.6     -0.40 
—  5.8    —0.45 
-  4.9     —0.40 
—  4.1     —0.35 

1800 
1600 
1400 
1200 
1000 

-  6.8    —  1.9 
—  6.0    -  1.4 
—  6.8    —  0.7 

—  4.6         0.0 
-  4.0         0.6 

—  8.8    —  8.0 
—  7.9    -  7.1 
—  6.8    —  6.0 
—  6.6    —  4.8 
—  4.6    —  8.8 

—  6.6    —  4.7 
—  4.9    —  4.1 
—  4.3    —  3.5 
—  3.9    —3.1 
—  3.4    -  2.6 

—  2.9          1.2 
-  2.3          1.8 
—  1.9         2.2 
-  1.6         2.5 
—  1.3          2.8 

—  8.4    —0.35 
—  2.7     -0.35 
—  2.0     —0.30 
—  1.4    —0.30 
—  0.8    —0.40 

800 
600 
400 
200 
0 

—  8.2          1.4 

—  2.4         2.2 
-  1.5         3.1 
—  0.7         3.9 
0.0         4.6 

—  8.4    —  2.6 
—  2.2    —  1.4 
—  1.2    —  0.4 
—  0.5         0.3 
0.0         0.8 

—  2.8    —  2.0 
—  2.8    -  1.5 
—  1.7    —  0.9 
-  0.8         0.0 
0.0         0.8 

—  0.9          3.2 
-  0.6          3.5 
—  0.4          3.7 
—  0.2          3.9 
0.0          4.1 

0.0    —0.35 
0.7    -0.35 
1.4    —0.30 
2.0    -0.30 
2.6     

Mean  gradient  up  to  4000  meters  —0.  40 

LOW  AREAS  IN  WINTER. 


Height 
In 
meters. 

North. 

East 

South. 

West 

Mean. 

AT            T 

AT            T 

AT            T 

AT           T 

T           ^ 
100 

6000 
5800 

,M-,.HI 

6400 
6200 
6000 

°C        °C. 
—83.4    —26.8 
—31.7    —24.8 
—29.8    —22.9 
—28.2    —21.3 
—27.0    —20.1 
—26.1    —19.2 

°C.         °C. 
—33.8    —29.6 
—32.4    —28.2 
—31.0    —26.8 
-29.7    —25.5 
—28.0    —23.8 
—26.6    —22.4 

°C.     •   °C. 
—34.4    —27.8 
—33.2    —26.6 
—32.0    —25.4 
—30.8    —24.2 
—29.2     —22.6 
—28.3    —21.7 

°  C.        °C. 
-35.5    -29.0 
—34.0    —27.5 
—32.8    —26.3 
-31.8    —25.3 
—31.0    -24.5 
—30.3    -23.8 

0  C.        °C. 
—28.2    —0.75 
—26.7    —0.70 
-25.3    -0.65 
—24.0     -0.65 
—22.7    —0.50 
—21.7    —0.50 

4800 
4600 
4400 
4200 
4000 

-24.8    —17.9 
—23.8    -16.9 
—22.5    -18.6 
—21.1     —14.2 
—19.9    —18.0 

—25.7    —21.5 
—24.  3     -20.  1 
—23.0    —18.8 
—21.4    —17.2 
—20.2    —16.0 

—26.9    -20.3 
—25.  8    —19.  2 
-24.2    —17.6 
-22.8     -16.2 
—22.0    —15.4 

—29.6    —23.1 
—28.8    —22.3 
—28.0    —21.5 
—26.9    -20.4 
—26.0    —19.6 

—20.7    —0.55 
—19.6    —0.65 
—18.3    —0.65 
—17.0    -0.55 
-15.9    —0.55 

3800 
3600 
3400 
3200 
8000 

—18.7    —11.8 
-17.4    —10.5 
-16.0    —9.1 
—14.7    —  7.8 
—13.5    —  6.6 

-19.0    —14.8 
—17.9     —13.7 
-16.5    —12.3 
—15.2    —11.0 
—14.2    —10.0 

—21.0    —14.4 
-20.0    —13.4 
—18.8    —12.2 
—17.7    -11.1 
-16.6    —10.0 

—24.7    —18.2 
-23.4    —16.9 
—22.  2    —15.  7 
-21.0    —14.5 
—19.7    -13.2 

-14.8     -0.60 
—13.6     -0.65 
-12.3    -0.60 
—11.1    —0.55 
—10.0    -0.66 

2800 
2600 
2400 
2200 
2000 

-12.5    —  5.6 
-11.8    —4.4 
—10.5    —  8.6 
—  9.8    —  2.9 
—  8.4    —  1.6 

—18.4    —  9.2 
—12.6    —  8.4 
-11.3     —7.1 
-10.2    —6.0 
—  9.2     -5.0 

—15.4    —  8.8 
—14.2    —  7.6 
—13.  0    —  6.  4 
-11.8    —  5.2 
-10.8     -  4.2 

—17.8    —11.3 
—15.9    —  9.4 
-14.6    —  8.1 
-13.1    —  6.6 
—12.0    —5.5 

—  8.  7    -0.  65 
—  7.4    —0.55 
—  6.3    -0.60 
—  5.  1    —0.  55 
—  4.  0    -0.  45 

1800 
1600 
1400 
1200 
1000 

—  7.8    —  0.9 
—  6.6         0.3 
—  5.8          1.1 
-5.4          1.5 
—  4.  8          2.  1 

—  8.  0    —  3.  8 
—  7.  0    —  2.  8 
-  5.9    —  1.7 
—  4.  7    —  0.  5 
—  3.  2          1.  0 

—  9.  8    —  3.  2 
-  8.8     -  2.2 
—  7.  7    —  1.  1 
—  6.4          0.2 
-5.2          1.4 

-11.0     -  4.6 
—10.0    —8.6 
—  8.  8    —  2.  3 
-  7.  8    —  0.  8 
—  6.0         0.5 

—  3.1    —0.56 
—  2.0    —0.50 
-  1.0    -0.60 
0.  2    —0.  65 
1.3    —0.50 

800 
600 
400 
200 
0 

—  a6          3.3 
-  2.4          4.5 
—  1.8          5.6 
—  0.6          6.3 
0.  0          6.  9 

—  2.6          1.6 
—  1.8         2.4 
—  1.  1         3.  1 
—  0.5         3.7 
0.0          4.2 

—  4.2          2.4 
—  3.  1          3.  5 
—  2.1          4.5 
-0.7          5.9 
0.  0          6.  6 

—  4.7          1.8 
—  3.  8         2.  7 
—  2.3          4.2 
-  0.9          5.  6 
0.  0          6.  5 

2.3    —0.50 
8.  3    -0.  55 
4.4    —0.50 
6.  4    —  0.  36 
6.1     

Mean  gradient  up  to  4000  meters  —  0.  65 

corded  in  column  four,  and  the  temperature  for  each  stratum 
is  computed  by  adding  the  temperature-falls  AT,  as  reduced 
to  centigrade  degrees,  to  the  surface  temperature  T.  At  the 
head  of  each  section  group  is  given  the  number  of  ascensions 
employed,  as  3  for  north,  9  for  east,  10  for  south,  etc.  In  the 
last  columns  of  each  general  group  are  given  the  mean  tempera- 


tures of  the  sectors  on  the  several  levels,  and  the  mean  gra- 
dients per  100  meters.  The  gradients  in  the  several  sectors 
can  be  readily  computed  from  the  temperatures  recorded  for 
every  200-meter  level  up  to  4000  meters.  It  should  be  noted 
that  the  data  are  entirely  lacking  for  the  north  sector,  except 
for  the  winter  high  areas,  where  three  ascensions  were  available, 
and  that  observations  in  the  central  area  are  found  only  for 
the  summer  half  of  the  year.  This  failure  to  record  the 
temperature  in  the  north  sector  is  due  to  two  causes,  (1)  the 
general  passage  of  the  centers  of  pressure  to  the  north  of  Blue 
Hill,  and  (2),  especially,  the  class  of  winds  prevailing  in  that 
sector,  which  are  usually  unfavorable  for  kite  ascensions. 

For  the  European  cyclones  and  anticyclones  I  have  employed 
the  data  found  in  Grenander's  paper.  The  ternperature-falls 
in  winter  low  and  high  areas  at  Hald  and  Berlin  (Table  3)  were 
taken  from  the  tables  and  diagram  without  change.  For  these 
the  results  are  recorded  in  Tables  3  and  4,  where  J  T  is  the  tem- 
perature-fall from  the  surface  and  T  the  corresponding  tem- 
perature at  every  200-meter  level.  In  order  to  eliminate  the 
diurnal  variation  from  the  surface  mean  temperatures,  upon 
which  every  thing  depends,  it  was  necessary  to  interpolate  a 
few  of  the  missing  night  temperatures  as  in  Table  5. 

There  is,  of  course,  some  uncertainty  in  this  connection, 
but  not  nearly  enough  to  modify  the  conclusions  based  upon 
these  surface  means.  It  is  much  better  to  obtain  approximate 
mean  temperatures  for  the  24  hours  than  to  employ  those  be- 
longing exclusively  to  the  day  hours.  In  the  summer  months 
the  Hald  and  the  Berlin  temperatures  were  treated  separately 
(see  Table  4)  and  the  adopted  temperatures  are  the  mean 
values  of  the  two  stations  in  the  several  200-meter  levels.  The 
column  T  is  the  mean  of  the  Hald  and  Berlin  columns,  with 
interpolations,  and  A  T  is  computed  from  T. 

TEMPERATURE-FALLS  FROM  THE  SURFACE. 

There  are  two  ways  in  which  the  data  of  these  tables  can  be 
conveniently  arranged  for  discussion,  (1)  by  exhibiting  the 
temperature-falls  on  a  diagram,  and  (2)  by  constructing  the 
temperatures  prevailing  in  the  horizontal  sections  at  different 
elevations.  Fig.  1  represents  the  American  and  European 
temperature-falls  in  high  and  low  areas,  in  winter  and  sum- 
mer. It  shows  at  a  glance  that  the  high  areas  (full  lines)  are 
not  all  cold  as  compared  with  the  low  areas,  nor  the  low  areas 
(dotted  lines)  all  warm  as  compared  with  the  high  areas.  On 
the  other  hand  the  north  and  west  of  the  high  areas  are  warm, 
while  the  south  and  east  are  cold,  both  winter  and  summer.  In 
the  lower  levels,  1000  to  2000  meters,  there  is  some  entangle- 
ment of  the  gradient  lines,  and  while  there  may  be  a  tendency  for 
the  dotted  lines  of  the  low  areas  to  cross  the  full  lines  of  the  high 
areas  from  right  to  left,  there  is  nothing  very  decisive  about 
the  relation.  In  the  American  areas  the  temperatures  of  the 
high  areas  generally  have  a  small  gradient  in  the  levels  1000 
to  2000  meters,  and  there  is,  also,  some  indication  of  the  same 
tendency  in  the  European  high  areas.  Attention  is  directed 
to  chart  14,  International  Cloud  Report,  1898,  where  a  cor- 
responding vertical  change  in  the  velocities  was  recorded, 
indicating  that  this  stratum  has  a  steady  velocity  throughout 
its  depth  in  accordance  with  this  local  temperature  distribu- 
tion. In  the  winter  both  the  European  and  American  temper- 
atures have  about  the  same  extreme  differences,  approximately 
10°  C.  above  the  2000-meter  level,  though  below  it  the  Ameri- 
can exceed  the  European  by  about  4°  C.  The  American 
circulation  near  the  surface  in  winter  is  usually  more  active 
than  the  European.  In  the  summer  the  American  temperature 
divergence  seems  to  be  rather  less,  about  2°,  than  the 
European,  though  this  difference  may  really  be  due  to  an 
inadequacy  in  the  results  of  the  observations  in  hand,  and 
may  be  changed  by  increasing  their  number.  •  On  the  whole 
there  are  indications  that  the  temperature  spread  is  wider  at 
the  3000-meter  level  than  at  any  height  above  or  below,  and 
this  implies  that  the  local  circulation  is  greater  at  this  level 


FIG.  3. — The  Distribution  of  Temperature  in  the  High  and  Low  Pressure  Areas  of  North  America. 


fojht 


Wirvier 


J-tzgh          Low  High 


6000 


5OOO 


40OO 


5000 


2OOO 


1000 


ooo 


FIG.  4. —  The  Distribution  of  Temperature  in  the  High  and  Low  Pressure  Areas  of  Europe. 


Mey/it 


Jfigfr         L 


ow 


cooo 


.5000 


4000 


3OOO 


2OOO 


MOO 


000 


JANUARY,  1906. 


MONTHLY  WEATHEE  REVIEW. 


13 


TABLE  4. —  Temperature-falls  at  Hold  and  Berlin. 
HIGH   AREAS  IN   SUMMER   (APRIL  TO  SEPTEMBER). 


Height 
in 
meters. 

North. 

East. 

South. 

West 

Mean. 

Hold      Berlin        A  7           T 

Hold    Berlin         AT          T 

Itald    Berlin         AT1          T 

Hold      Berlin        AT          T 

y                   AT 

100 

6000 
5800 
5600 
5400 
5200 
5000 

°  C.         °  C.        °  C.        °  C. 
—15.9    -17.5     -30.4    —16.7 
—29.  2     -15.  5 
—27.9      -14.2 
—26.7    —13.0 
—25.5    —11.8 
—  9.7    —11.5    —24.3     —10.6 

°  C.        °  C.       °  C.       °C. 
—25.  4    —23.  1    —35.  6    -24.  3 
—34.0    —22.7 
—32.  4    —21.  1 
—31.  0    —19.  7 
—29.  7     —18.  4 
—18.5    —15.9    —28.5    —17.2 

°  c.      °c.     °c.     °a 

-18.2    -19.5    —31.7    —18.9 
-30.5    —17.7 
—29.  3    —16.  5 
-28.1     —15.3 
—27.  0    —14.  2 
—12.2    —14.0    —25.9    —18.1 

°  C.        °C.       °C.       °  C. 
—16.4    —16.9    —30.7    —16.7 
—29.  4    —15.  4 
-28.0    -14.0 
—26.7    —12.7 
—25.4    —11.4 
—  9.6    —10.7    —24.2     —10.2 

°  c.      °  c. 

-19.2    -0.65 
—17.  9    -0.  65 
—16.  6    —0.  65 
—15.  3    —0.  65 
—14.0    —0.60 
—12.  8    —0.  60 

4800 
4600 
4400 
4200 
4000 

—23.  2    —  9.  5 
—22.  1     —  8.  4 
—20.  9     -  7.  2 
—19.  7    —  6.  0 
—  3.  6    —  6.  0    —18.  5    —  4.  8 

—27.3    —16.0 
—26.  1    —14.  8 
—24.  9    —13.  6 
—  23.  7    —12.  4 
—12.8    -  9.6    —22.5    —11.2 

-24.9     -12.1 
—23.8     —11.0 
-22.  7    —  9.  9 
—21.  6    —  8.  8 
—  6.  4    —  9.  0    —20.  5    —  7.  7 

-22.  9    —  8.  9 
—21.  6     —  7.  6 
—20.4    —6.4 
—19.  3    —  5.  3 
—  4.  5    —  3.  9    —18.  2    —  4.  2 

—11.6    —0.60 
—10.4    —0.60 
—  9.  2    —0.  60 
—  8.  1    —0.  55 
—  7.  0    —0.  50 

3800 
3600 
3400 
3200 
3000 

—17.3    —  3.6 
—16.  2    —  2.  6 
—15.3    —  1.6 
-14.  6    —  0.  9 
1.2    —  2.0    —14.1    —  0.4 

—21.3    -10.0 
—20.  2    —  8.  9 
—19.  3    —  8.  0 

—18.5    —7.2 
—  8.  5     -  4.  5    —17.  8     -  6.  5 

—19.  2    —  6.  4 
—17.9     —  5.1 
—16.7    —3.9 
-  15.  5     -  2.  7 
—  0.  7     —  2.  6    —14.  5    —  1.  7 

—17.  2    —  3.  2 
-16.2    —2.2 
—15.2    —  1.2 
—14.  2    —  0.  2 
0.1           1.5     -13.2          0.8 

—  6.  0    —0.  55 
—  4.  9    —  0.  50 
—  3.  9    —0.  50 
—  2.  9    —0.  45 
—  2.  0    —  0.  40 

2800 
2600 
2400 
2200 
2000 

—13.  5          0.  2 
—12.  9         0.  8 
—12.3          1.4 
—11.7          2.0 
4.5          0.8    —11.0          2.7 

—17.  3    —  6.  0 
—16.  9     —  8.  6 
—16.2    -  4.9 
—15.  3     —  4  0 
—  5.  4    —  0.  3    —14.  1    —  2.  9 

—13.  6    —  0.  8 
—12.  8          0.  0 
—12.  1         0.  7 
-11.2         1.6 
3.7          1.5    —10.2          2.6 

—12.  1           1.  9 
-11.0          3.0 
—10.  0          4.  0 
—  9.  0         5.  0 
6.  2         6.  6    —  8.  1          5.  9 

—  1.2    —0.  40 
—  0.  4    —0.  40 
0.4    —0.40 
1.2    —0.45 
2.  1     -0.  45 

1800 
1600 
1400 
1200 
1000 

—10.  3          3.  4 
—  9.  6          4.  1 
—  8.8          4.9 
—  7.  9          5.  8 
7.  4          6.  1     -  6.  9          6.  8 

—12.9    —  1.6 
—11.  6    —  0.  3 
—10.  2          1.  1 
—  8.9          2.4 
2.2         5.3—7.5         3.8 

—  9.  3          3.  6 
—  8.  3          4.  5 
—  7.4          6.4 
—  6.  4          6.  4 
7.  2         7.  5    —  5.  4         7.  4 

—  7.4         6.6 
—  6.  6         7.  4 
—  5.  8         8.  2 
—  5.  0         9.  0 
8.4        11.1     -4.2          9.8 

3.0    —0.50 
4.  0    —  0.  45 
4.9    —0.50 
5.9    —0.55 
7.0    —0.60 

800 
600 
400 
200 
0 

—  5.  7         8.  0 
—  4.  5          9.  2 
—  3.  2        10.  5 
—  1.7        12.  0 
13.5        13.9    —  0.0        13.7 

—  6.  1          6.  2 
—  46          6.  7 
—  3.  1          8.  2 
—  1.  6          9.  7 
9.1         13.5          0.0        11.3 

—  4.  4          8.  4 
-3.3          9.5 
-  2.  2        10.  6 
—  1.1         11.7 
10.5        15.1          0.0        12.8 

Mean  gradient  up  to  4000  m 

—  3.  3        10.  7 
—  2.5        11.5 
—  1.6        12.5 
—  0.  8        13.  2 
11.4        16.5         0.0        14.0 

8.2    —0.55 
9.3    —0.60 
10.5    —0.60 
11.  7    —0.  65 
13  0 

—0.60 

LOW  AREAS  IN  SUMMER. 


6000 
5800 
5600 
5400 
5200 
5000 

—17.  0    —  9.  5    —30.  1    —13.  3 
—29.  0    —12.  2 
—27.9    —11.1 
-26.  7    —  9.  9 
—25.6    —8.8 
—12.1    —  3.5    —24.6    —  7.8 

—18.9    —17.5    —35.5    —18.2 
—34.  1     —16.  8 
—32.8    —15.5 
—31.4    —14.1 
—30.  1    —12.  8 
—11.9    —11.3    —28.9    —11.6 

—22.0    —21.8    —35.4    —21.9 
—34.3    —20.8 
—33.1    —19.6 
—31.9    —18.4 
—30.7    —17.2 
-16.8    —15.9    —29.6    —16.1 

—  248    -21.4    —36.0    —  2aO 
—35.  3    —21.  9 
-34.1    —20.7 
—32.  9    —19.  5 
—31.7    —18.3 
—  19.3    —14.8    —30.5    —17.1 

—18.  1    —0.  50 
—17.1    —0.45 
—16.2    —0.50 
—15.  2    —0.  50 
—14.2    —0.60 
—13.  2    —0.  55 

4800 
4600 
4400 
4200 
4000 

—23.  8    —  7.  0 
—22.  9    —  6.  1 
-21.  8    —  5.  0 
—20.  7    —  3.  9 
—  7.  5          2.  0    —19.  6    —  2.  8 

—27.7    —10.4 
—26.  5    —  9.  2 
—25.  4    —  8.  1 
—24.  3    —  7.  0 
—  6.  4    —  5.  4    —23.  2    —  5.  9 

—28.5    —15.0 
—27.4    —13.9 
—26.  3    —12.  8 
—25.2    —11.7 
—11.0    —10.2    —24.1     —10.6 

—29.2    —15.8 
—27.9    -14.5 
—26.5    —13.1 
—25.  2    —11.  8 
—12.  7    —  8.  2    —23.  9    —10.  5 

—12.  1    —0.  55 
'  —11.  0    —0.  60 
—  9.  8    —0.  60 
—  8.  6    —  0.  55 
—  7.5    —0.50 

3800 
3600 
3400 
3200 
3000 

—18.7    —  1.9 
—  17.8    —  1.0 
—16.8          0.0 
—15.8          1.0 
—  3.  1          7.  0    —14.  8          2.  0 

—22.  2    —  4.  9 
—21.  1    —  3.  8 
—20.  1    —  2.  8 
—19.1     —1.8 

—  1.5       o.o  —18.1  —  0.8 

—23.  1     —  9.  6 
—22.  2    —  8.  7 
-21.  3    —  7.  8 
—20.4    —  6.9 
—  5.  8     -  5.  9    —19.  4    —  5.  9 

—22.  8    —  9.  4 
—21.  7    —  8.  8 
—20.  5    —  7.  1 
—19.  3    —  5.  9 
—  6.4    —  3.0    —18.1    —  4.7 

—  6.  5    —0.  50 
—  5.  5    —0.  55 
—  4.  4    —0.  50 
—  3.  4    —0.  50 
—  2.  4    —  0.  50 

2800 
2600 
2400 
2200 
2000 

—14.  0          2.  8 
—18.  2          3.  6 
—12.  3          4.  5 
—11.4          5.4 
1.2        11.8    —10.4          6.4 

—17.  2          0.  1 
—16.3          1.0 
—15.  4          1.  9 
—14.  3         3.  0 
4.0          4.4    —13.1          4.2 

—18.  3    —  4.  8 
—17.  2    —  3.  7 
—16.  1    —  2.  6 
—15.  0—1.5 
—  0.  2    —  0  5    —13.  9    —  0.  4 

—16.  9    —  3.  6 
—15.  8    —  2.  4 
—14.  7    —  1.  3 
—13.6    —0.2 
—  0.  9          2.  7    —12.  5          0.  9 

—  1.4    —0.46 
—  0.  5    —0.  50 
0.6    —0.55 
1.6    —0.60 
2.8    —0.60 

1800 
1600 
1400 
1200 
1000 

—  9.  2          7.  6 
—  8.  0          8.  8 
—  6.  7        10.  1 
—  5.4        11.4 
6.  3        18.  7    —  4.  3        12.  5 

—11.5          5.8 
—  9.  8          7.  5 
—  8.  1          9.  2 
—  6.  6        10.  7 
10.  2        13.  7    —  5.  3        12.  0 

—12.  8          0.  7 
—11.6          1.9 
—10.  4          3.  1 
—  9.  1          4.  4 
5.  2          6.  2    —  7.  8          6.  7 

—11.4         2.0 
—10.  4         8.  0 
—  9.  2         4.  2 
—  8.  0         6.  4 
4.  3         9.  0    —  6.  7          6.  7 

4.0    —0.60 
5.  3    —0.  65 
6.6    —0.65 
7.  9    —0.  65 
9.2    —0.65 

800 
600 
400 
200 
0 

—  3.  4        13.  4 
—  2.  5        14.  3 
—  1.7        15.  1 
—  0.  8        16.  0 
12.4       21.2         0.0        16.8 

—  4.  2        13.  1 
—  3.  2        14.  1 
—  2.  1         15.  2 
—  1.0        16.  3 
14.9        19.6          0.0        17.8 

—  6.  4          7.  1 
—  4.  8          8.  7 
—  3.  3        10.  2 
—  1.7        11.8 
13.0        14.0          0.0        13.6 

Mean  gradient  up  to  4000  m 

—  5.  3         8.  1 
—  4.  0         9.  4 
—  2.  7        10.  7 
—  1.  4        12.  0 
12.4        14.4         0.0        13.4 

10.4    —0.60 
11.6    —0.60 
12.9    —0.65 
14.  1    —0.  60 
15.3     

—0.67 

than  above  or  below  it,  a  result  indicated  by  the  observed 
velocities  as  shown  on  chart  68  of  my  Cloud  Report.  It  is 
hardly  possible  to  consider  the  temperatures  for  the  upper 
levels,  4000  to  6000  meters,  as  sufficiently  reliable  to  base  special 
emphasis  upon  the  wide  divergence  of  the  European  tempera- 
tures in  those  levels,  and  the  lines  should  probably  be  drawing 
together  more  rapidly  than  here  shown.  From  other  consid- 
erations it  may  be  inferred  that  the  temperature  differences 
generally  disappear  in  the  neighborhood  of  the  cirrus  levels 
9000  to  10,000  meters.  While  there  is  a  tendency  in  the  lower 
levels  for  the  temperatures  of  the  high  areas  to  diminish  less 
rapidly  than  those  of  the  low  areas,  there  is  yet  but  little  to 


justify  the  view  that  anything  like  an  inversion  of  tempera- 
ture occurs,  such  as  Professor  Hann  found  in  mountain  stations 
and  ascribed  to  dynamic  actions,  or  such  as  Bjerknes  and 
Clayton  assume  to  exist  in  their  theories  of  cold-center  and 
warm-center  cyclones  superposed  upon  each  other.  This  will 
be  seen  more  clearly  in  the  exhibit  of  figs.  3  and  4.  We 
may  safely  infer  from  fig.  1  that  there  is  little  to  distinguish 
the  temperature  distribution  in  European  cyclones  and  anti- 
cyclones from  that  prevailing  in  the  American  high  and  low 
areas. 

Using  the  same  temperature-falls  we  now  discuss  the  rela- 
tion according  to  actual  warm  and  cold  areas,  as  shown  in 


14 


MONTHLY  WEATHER  REVIEW. 


JANUARY,  1906 


fig.  2,  where  the  dotted  lines  indicate  the  warm  areas  and  the 
full  lines  the  cold  areas.  Hence  we  adopt  the  following 
arrangement:  (See  Table  6.)  . 

TABLE  5. — Surface  temperatures  in  centigrade  degrees  for  day  and  night  at 
Hald  and  Berlin. 

HIGH  AREAS. 


Station. 

W 

nter. 

Summer. 

Hald  j 

Berlin 
Mea 

day         

N. 
6.1 

2.1 

6.6 
4.6 

4.6 

E. 
8.8 
(0.0) 

1.7 
2  5 

& 

1.1 
-1.7 

1.9 

1.8 

0.8 

w. 

1.3 
6.1 

4.2 
5.9 

4.1 

N. 
14.9 
(12.0) 

17.1 
10.6 

13.7 

1'j. 
10.4 
(7.8) 

16.6 
10.8 

11.3 

S. 
14.0 

(6.9) 

18.5 
11.6 

12.8 

W. 
12.6 
(10.2) 

19.0 
14.0 

14.0 

/day                           ..  .. 

(night 

0.8 

LOW  AREAS. 


JV. 
6.1 

E. 
6.6 

& 

6.2 

W. 
4.6 

N. 
146 

E. 
15.8 

8. 
14.0 

W. 
12.8 

Hmld  {Sight.  ...::;:::::::.:.::: 

(4.0) 

3.7 

6.0 

6.8 

10.1 

14.0 

12.0 

(12.0) 

12.8 

2.7 

8.6 

9.2 

26.5 

20.9 

15.5 

14.9 

Berlin  {night 

4.7 

4.7 

(6.6) 

(6.6) 

15.8 

18.8 

12.5 

(14.0) 

Means       

6.9 

4.2 

6.6 

6.5 

16.8 

17.3 

18.6 

13.4 

TABLE  6.— Distribution  of  the  sectors  by  warm  and  cold  areas. 


Blue  Hill,  winter. 


Hald  and  Berlin,  winter. 


Warm  areas. 

Cold  areas. 

Warm  areas. 

Cold  areas. 

High  north. 
High  west. 
Low  east. 
Low  south. 

High  east. 
High  south. 
Low  west. 
Low  north. 

High  north. 
High  south. 
High  west. 
Low  north. 

High  east. 
Low  east. 
•  Low  south. 
Low  west. 

Blue  Hill,  summer. 

Hald  and  Berlin,  summer. 

High  north. 
High  west. 
Low  east. 
Low  south. 

High  east. 
High  south. 
Low  north. 
Low  west. 

High  north. 
High  west. 
Low  north. 
Low  east. 

High  east. 
High  south. 
Low  south. 
Low  west. 

This  summary  shows  that  as  a  whole  the  warm  and  cold 
temperatures  are  about  equally  distributed  between  the  high 
areas  and  low  areas,  especially  in  the  levels  above  1000  meters. 
Below  that  level,  in  the  stratum  near  the  ground,  there  is 
much  less  regularity  in  the  distribution,  and  this  probably 
means  that  the  true  cyclonic  and  anticyclonic  action  is  dis- 
turbed by  coming  in  contact  with  the  ground,  and  by  the 
adjustment  to  surface  conditions.  It  also  shows  that  the  surface 
temperatures  are  not  entirely  reliable  as  records  of  the  real  distribu- 
tion prevailing  in  the  free  air,  and  it  implies  that  for  accurate  fore- 
casting it  will  be  necessary  to  change  from  the  exclusive  use  of  sur- 
face temperature  charts  to  those  determined  by  observations  in  the 
free  air  at  somewhat  moderate  elevations,  such  as  can  be  easily 
obtained  by  kite  flights  up  to  1000  or  2000  meters. 

TEMPERATURE    DIFFERENCES    AT    THE    SAME    ELEVATION. 

The  results  of  the  computations  may  be  exhibited  even 
more  clearly  by  plotting  the  temperatures  on  the  several  1000- 
meter  levels,  and  drawing  a  line  to  separate  the  high  tempera- 
ture from  the  low  temperature  regions.  Fig.  3  shows  the 
distribution  for  the  American  and  fig.  4  for  the  European 
cyclonic  and  anticyclonic  regions.  The  loss  of  the  data  in  the 
north  sector  of  the  American  cyclone  makes  this  line  of  demar- 
cation uncertain  in  that  area,  but  by  analogy  with  the  European 
data  and  from  what  we  know  of  conditions  at  the  surface  it  is 
probably  quite  like  that  indicated  in  the  diagram.  In  spite  of 
the  fact  that  we  have  been  using  an  insufficient  amount  of 
observations  to  render  the  temperature  distribution  entirely 
normal,  it  is  yet  evident  that  the  distribution  is  fundamentally 
the  same  in  the  American  and  European  circulation.  There  is  an 
inflow  of  cold  air  from  the  northwest  between  the  centers  of  baro- 


metric high  and  low  pressure,  and  an  inflow  of  warm  air  from  the 
south,  likewise  between  the  centers  of  low  and  high  pressure.  There 
are  no  cold-center  anticyclones  in  any  level,  nor  any  warm-center 
cyclones  in  any  level.  There  is  no  inversion  of  type  from  the  sur- 
face to  the  highest  level  reached,  with  the  possible  exception  of  the 
surface  and  the  1000-meter  level  of  the  European  cyclones  in  the 
winter.  I  am  at  a  loss  to  explain  this  last  result,  and  suspect 
that  it  may  be  due  to  our  imperfect  elimination  of  the  diurnal 
temperature  variation  from  the  data  contained  in  Grenander's 
paper,  or  in  the  Hald  and  Berlin  reports.  This  exception  seems 
to  constitute  the  basis  for  the  claim  that  has  been  advanced 
for  Professor  Hann's  theory  that  the  warm-center  cyclone 
below  is  replaced  by  a  cold-center  cyclone  above,  and  that  this 
inversion  of  temperature  implies  a  dynamic  system  as  the 
source  of  the  level  cooling.  The  fact  is  that  the  cool  north- 
west winds  in  the  upper  levels  follow  the  stream  lines  marked 
out  in  the  diagrams  of  the  Weather  Bureau  International  Cloud 
Report,  as  given  in  chart  15,  or  in  the  MONTHLY  WEATHER  REVIEW, 
March,  1902.  They  become  more  and  more  sinuous  in  descending 
from  the  cirrus  levels  to  the  surface,  or  below  the  strato-cumulus 
level,  3000  meters,  curling  more  decidedly  in  an  anticyclonic  rota- 
tion with  a  tendency  to  divide  into  two  branches.  The  southerly 
winds  in  the  same  way  divide  into  two  branches  one  curling  into 
the  cyclone  on  the  northeast  and  the  other  into  the  anticyclone  on  the 
northwest  of  the  respective  centers. 

The  mechanical  cyclone  and  anticyclone,  with  centers  of  high 
and  low  pressure  at  the  boundary  between  these  cold  and  warm 
currents,  are  the  dynamic  effect  of  the  vertical  and  horizon- 
tal motion  of  these  currents  of  different  temperature,  just  as 
has  been  explained  in  my  previous  papers.  The  observed  vec- 
tors of  velocity  are  such  as  to  produce  or  accompany  the  tem- 
perature distribution  here  described,  and  the  cold  and  the  warm 
currents  having  different  temperatures  bear  within  themselves 
the  source  of  the  energy  of  storms.  The  fact  is  that  storms 
are  produced  by  horizontal  convection  more  than  by  vertical  convec- 
tion. The  latent  heat  of  condensation  is  an  additional  source 
of  energy,  and  the  underflowing  of  warm  currents  beneath  the 
eastward  drift  is  another  small  source  of  energy,  but  these 
are  distinctly  subordinate  to  the  horizontal  or  lateral  convec- 
tion between  these  counterflowing  masses  or  sheets  of  air. 
The  cyclone  and  anticyclone  are  the  dynamic  effects  of  this  ther- 
modynamic  energy,  and  this  function  constitutes  the  true  prob- 
lem in  meteorology  for  study.  It  is,  therefore,  evident  that  the 
different  statements  found  in  the  literature  of  the  subject 
regarding  the  cyclone  being  cooler  than  the  anticyclone  in  the 
upper  levels,  have  been  imperfect  and  rough  efforts  to  reach 
the  facts  here  shown.  Since  the  counterflow  does  have  some- 
what different  configurations  in  the  several  levels,  there  is  a 
difference  of  temperature  to  be  obtained  on  proceeding  from 
the  surface  upward  over  the  same  sector.  But  it  is  not  proper 
to  compare  the  temperatures  of  cyclones  as  a  whole,  from  level 
to  level,  nor  of  anticyclones,  without  careful  discrimination  as 
to  the  subareas  which  are  involved.  It  is  important,  likewise, 
to  obtain  the  gradients  over  the  warm  and  cold  areas,  sepa- 
rately, rather  than  over  the  cyclones  and  anticyclones  taken 
as  wholes,  as  was  done  in  Tables  1,  2,  3,  4. 

VERTICAL  TEMPERATURE  GRADIENTS  PER   100  METERS. 

Taking  the  mean  gradients  over  the  high  areas  and  the  low 
areas  for  the  American  and  European  temperatures,  and  lim- 
iting the  means  to  the  4000-meter  level  for  the  sake  of  the 
comparison,  we  obtain  from  Tables  1,  2,  3,  4: 


Winter. 


High  areas. 

Low  areas. 

High  areas. 

Low  areas. 

American  

0  F. 
—  0.42 
—  0.40 

°  F. 
—  0.43 
—  0.56 

American    .... 
European  

0  F. 
—  0.62 
—  0.60 

0  F. 

—  0.63 
—  0.57 

Summer. 


JANUARY,  1906.  MONTHLY  WEATHER  REVIEW. 

TABLE  7. —  Temperatures  and  gradients  in  the  American  and  European  cyclones  and  anticyclones  arranged  by  the  warm  and  cold  areas. 


15 


Blue  Hill,  winter. 

Hald  and  Berlin,  winter. 

Blue  Hill,  summer. 

Hald  and  Berlin,  summer. 

Height 

in 
meters. 

Warm. 

Cold. 

Warm. 

Cold. 

Warm. 

Cold. 

Warm. 

Cold. 

0  C.        °C. 

°c.      °c. 

0  C.        °G 

°C.        °C 

0  C.        °  C. 

°  C.        °C. 

0  C         °  C. 

0  C.        °  C. 

6000 

—24.  9    —0.  75 

—29.0    —0.70 

-16.2    —0.60 

—22.0    —0.60 

5800 

—23  4     —0  80 

—28  5    —0  70 

—15.  0    —0.  65 

—  20.  8    —  0.  65 

5600 

—21.8    —0.70 

—27.1    —0.70 

—13.7     —0.65 

-19.5    —0.65 

5400 

20  4    —  0  65 

25  7        9  65 

—12.4    —0.60 

—18.2    —  0.60 

5200 

—19.1     —0.60 

—24.2    —0.60 

—11.2    —0.55 

—17.0    —0.55 

5000 

—17.9     —0.55 

—23.0    —0.55 

—  10.  1    —0.  55 

—15.9    —0.60 

4800 

—16  8    —  0  60 

—21.9     —0.  60 

—  9.0    —0.60 

—14.7     —0.55 

4600 





-15.6    —0.65 

-20.7    —0.60 

—  7.8    —0.55 

—13.6    —0.60 

4400 

—14  3    _0  65 

—19  5    —0.60 

—  6.7    —0.55 

—12.4    —0.60 

4200 

—13.0    -0.60 

—18.3    —0.55 

—  5.6    —0.60 

—11.2    —0.60 

4000 

—ii.9  Hoiso 

—17.6    —0.55 

—11.8    —0.50 

—17.2    —0.50 

—  4.3    Ho."  70 

—  9.2    HO.  70 

—  4.4    —0.50 

-10.0    —0.55 

3800 

-10.9    —0.45 

—16.5    —0.55 

—10.8    MJ.55 

—16.2    —0.55 

—  2.9    —0.60 

—  7.8     —0.65 

—  3.4    —0.50 

—  8.9    —0.55 

3600 

—10.0    —0.50 

—15.4    —0.50 

—  9.7    —0.55 

—15.1    —0.55 

—  1.7    —0.65 

—  6.5    —0.75 

—  2.4    —0.50 

—  7.8     —0.55 

3400 

—  9.0     -0.50 

—14.4     —0.60 

—  8.6    —0.55 

—14.0     -0.60 

—  0.4    —0.60 

—  5.0    —0.70 

—  1.4    —0.50 

—  6.7    —0.50 

8200 

—  8.0    —0.55 

—13.4    —0.55 

—  7.5    —0.55 

-12.8    —0.60 

0.8    —0.65 

—  3.6    -0.70 

_  0.4    —0.40 

—  5.7    —0.50 

3000 

—  6.9    —0.45 

—12.3    —0.50 

-  6.4    —0.40 

—11.6    —0.60 

2.1    —0.55 

—  2.2    —0.65 

0.4     -0.45 

—  4.7    -0.45 

2800 

—  6.0    —0.45 

—11.3    —0.45 

—  5.6    —0.40 

—10.4    —0.60 

3.2     —0.60 

—  0.9    —0.70 

1.3    —0.40 

—  3.8    —0.45 

2600 

—  5.1     —0.45 

-10.4    -0.50 

—  4.8     -0.40 

—  9.2    —0.55 

4.4    —0.55 

0.5    —0.65 

2.1    —0.40 

—  2.9     —0.45 

2400 

—  4.2    —0.50 

_  9.4    —0.40 

_  4.0    —0.40 

—  8.1    —0.60 

5.5    —0.60 

1.8    —0.65 

3.0    —0.45 

—  2.0    —0.50 

2200 

—  3.2    —0.45 

—  8.6     -0.45 

—  3.2    -0.45 

—  6.9    —0.50 

6.7    —0.55 

3.1     —0.65 

3.9    —0.45 

—  1.0    —0.55 

2000 

-  2.3    —0.50 

-7.7    —0.40 

—  2.3    —0.35 

—  5.9    —0.50 

7.8    —0.60 

4.4    —0.60 

4.8    —0.55 

0.1    —0.55 

1800 

-  1.3    —0.50 

—  6.9    —0.40 

—  1.6    —0.35 

—  4.9    —0.50 

9.0    —0.50 

5.6    —0.70 

5.9     -0.55 

1.2    —0.55 

1600 

—  0.3    —0.25 

—  6.1     —0.40 

—  0.9    —0.35 

—  3.9    —0.60 

10.0    —0.55 

V.O    —0.65 

7.0    —0.55 

2.3    —0.60 

1400 

0.2    —0.15 

—  5.4     —0.35 

—  0.2     —0.20 

—  2.7     -0.60 

11.1    —0.50 

8.3    —0.65 

8.1    —0.55 

3.5    —0.60 

1200 

0.5     —0.20 

—  4.8    —0.30 

0.2     —0.25 

—  1.5    —0.60 

12.1     —0.45 

9.6    -0.40 

9.2     -0.55 

4.7    —0.60 

1000 

0.9    —0.20 

-  4.6    —0.10 

0.7     —0.40 

—  0.3    —0.55 

13.0    —0.40 

10.4    —0.40 

10.3    —0.50 

5.9     -0.65 

800 

1.3    —0.35 

_  4.8    —0.15 

1.5    —0.35 

0.8    —0.50 

13.8    —0.55 

11.2    —0.50 

11.8    —0.50 

7.2    —0.70 

600 

2.0     -0.50 

—  3.8    —0.25 

2.2    —0.35 

1.8     —0.55 

14.9    —0.55 

12.2    —0.60 

12.3    —0.50 

8.6    —0.65 

400 

3.0    —0.65 

—  2.9    -0.55 

2.9    —0.30 

2.9    —0.40 

16.  0     —0.  70 

13.4    —0.60 

13.3     —0.55 

9.9    —0.70 

200 

4.2    —0.65 

—  1.8    —0.65 

3.5    —0.30 

3.7    —0.35 

17.4    —0.65 

14.6    —0.55 

14.4    -0.55 

11.3    —0.75 

0 

5  5 

0  5 

4  1 

4  4 

18  7 

15  7 

15  5 

12  8 

The  American  mean  gradient  is  about  the  same  for  high  and 
low  areas  at  all  seasons  of  the  year,  though  the  summer 
gradient  is  greater  than  the  winter  in  the  ratio  of  3  to  2. 
This  is  a  function  of  the  observed  difference  of  velocity  for 
these  two  seasons.  The  European  gradient  is  larger  in 
cyclones  than  in  anticyclones  for  both  seasons,  and  there  is 
not  so  much  difference  between  them  in  the  summer  as  in  the 
winter.  These  variations  depend  upon  the  local  conditions 
which  control  the  origin  and  mixing  of  the  countercurrents 
themselves.  Surveying  the  gradient  lines  as  a  whole,  I  believe 
that  they  show  that,  after  escaping  from  the  surface  confusion, 
the  lines  spread  gradually  up  to  3000  meters,  or  the  strato-cumu- 
lus  level,  where  the  difference  is  a  maximum  and  that  they  then 
draw  slowly  together  up  to  about  the  cirrus  level  where  the  east- 
ward drift  is  usually  undisturbed.  This  conforms  to  my  solu- 
tion obtained  for  the  local  cyclonic  velocities,  which  showed 
that  the  maximum  gyration  is  in  the  cirro-cumulus  level,  and 
that  it  diminishes  downward  and  upward  without  reversal?  The 
discussion  of  these  velocities  and  temperatures,  together  with 
the  corresponding  pressures  will  be  undertaken  in  a  later 
paper  of  this  series.  It  is  now  evident  that  any  adiabatic  solu- 
tion of  the  problem  is  inadequate,  and  that  the  omission  of 
the  heat  added,  J  Q—0,  is  fatal  to  a  satisfactory  discussion  of 
natural  cyclones  and  anticyclones,  because  the  observed 
gradients  differ  from  the  adiabatic  gradient,  0.987  degree 
centigrade  per  100  meters.  Furthermore,  the  surrounding 
of  fixed  masses  of  air  with  artificial  boundaries  for  the  sake 
of  a  ready  integration,  also  takes  the  problem  out  of  the  class 
of  those  required  in  meteorology,  and  makes  merely  special 
ideal  cases  which  are  out  of  our  consideration.  It  has 
seemed  to  me  proper  to  wait  for  the  acquisition  of  approximate 
values  of  the  velocity,  temperature,  and  pressure  before  try- 
ing to  do  anything  with  the  analytical  solutions.  Since  it  is 
the  divergence  of  the  local  temperatures  away  from  the  mean 
temperature  of  the  atmosphere  which  produces  the  local  cir- 
culations, we  should  evidently  compute  the  gradients  in  the 
warm  and  cold  areas  regardless  of  their  distribution  around 
the  centers  of  pressure. 

5  Compare  chart  68,  International  Cloud  Report,  flgs.  6,  7;  and  Tables 
11,  12,  Monthly  Weather  Review,  March,  1902. 


TABLE  8. — Temperature  differences,  cold  minus  warm  areas. 


Winter. 

Summer. 

Blue  Hill. 

Hald  and  Berlin. 

Blue  Hill. 

Hald  and  Berlin. 

°  F. 

0  J?. 

Of 

°^. 

6000 

—5.0 

—5.8 

5000 

-5.1 

—5.8 

4000 

-5.7 

—5.4 

—4.9 

-5.6 

3000 

—5.4 

-5.2 

-4.3 

—5.1 

2000 

—5.4 

—3.6 

—3.4 

—4.7 

1000 

—5.5 

-1.0 

—2.6 

-4.4 

0 

-6.0 

+0.3 

—3.0 

—2.7 

VERTICAL  TEMPERATURE  GRADIENTS  IN  THE  WARM  AND  COLD  AREAS. 

By  taking  the  mean  temperatures  at  the  different  levels, 
arranged  according  to  the  warm  and  cold  area  groups  indi- 
cated in  Table  6,  we  obtain  the  temperatures  and  gradients  of 
Tables  7  and  8.  There  are  several  results  which  can  be  readily 
seen  on  the  face  of  the  tables:  (1)  The  temperatures  at  Blue 
Hill,  Hald  and  Berlin  are  in  sufficient  agreement  as  to  the  ab- 
solute values  in  the  several  levels,  to  enable  us  to  infer  that  the 
American  and  Eviropean  systems  are  in  harmony  so  far  as  the 
temperature  is  concerned.  (2)  The  difference  between  the 
temperatures  in  the  warm  and  cold  areas  is  about  5.4°  on  the 
4000-meter  level,  and  it  diminishes  toward  the  surface,  except 
at  Blue  Hill  in  winter.  For  Hald  and  Berlin  in  winter  there 
is  the  anomalous  inversion  already  mentioned.  For  summer, 
at  all  stations,  the  temperature  difference  is  about  3°  in  the 
lower  levels.  (3)  The  gradient  at  Blue  Hill  in  winter  is 
— 0.65°  near  surface,  — 0.20°  at  the  1000-meter  level,  and 
— 0.50°  at  4000.  meters.  Hald  and  Berlin  show  a  compara, 
tively  steady  increase  of  the  gradient  from  the  surface- 
— 0.35°,  to  — 0.75°  at  6000  meters,  with  a  slight  diminution 
in  the  1000  to  2000-meter  stratum  for  the  warm  areas;  in  the 
cold  areas  the  gradient  is  about  — 0.60°  in  the  upper  levels 
throughout  a  deep  stratum.  In  summer  the  gradient  at  the 
surface  is  about  — 0.60°,  at  the  1000-meter  level  — 0.40°,  and 
at  4000  meters  —0.65,  at  Blue  Hill;  at  Hald  and  Berlin  there 
is  a  diminution  of  the  gradient  up  to  the  3000-meter  level  and 
an  increase  up  to  the  6000-meter  level  for  warm  and  cold  areas. 
These  facts  are  of  special  significance  in  the  thermodynamics  of 


16 


MONTHLY  WEATHER  REVIEW. 


JANUARY,  1906 


cyclonic  circulations.  These  temperature  gradients  may  profit- 
ably be  compared  with  the  gradients  in  high  or  low  pressure 
areas  taken  as  a  whole.  The  departure  of  the  temperature  in 
each  sector  from  the  prevailing  mean  air  temperature  is  evi- 
dently the  basis  for  a  thermodynamic  discussion  of  the  cyclonic 
problem. 

RESULTS. 

We  conclude  that  there  is  no  fundamental  difference  in  the 
structure  of  American  and  European  cyclones  and  anticyclones. 
The  observed  temperature  distribution  is  in  harmony  with 
the  observed  atmospheric  currents,  and  is  due  to  an  intermix- 
ture of  currents  from  warm  and  cold  latitudes,  the  energy  of 
storms  being  thus  referred  to  the  heat  transported  from  differ- 
ent latitudes.  The  pressure  centers  of  motion  occur  on  the 
boundaries  of  these  countercurrents,  and  thus  represent  the 
dynamic  effects  of  the  thermodynamic  energy.  Instead  of  ver- 
tical convection  being  the  primary  cause  of  storms  it  is  rather 
horizontal  convection,  interchange  of  heat  energy  on  the  same 
levels,  as  suggested  in  my  preceding  papers.  There  is  no  evi- 
dence of  the  superposition  of  cold-center  cyclones  upon  warm- 
center  cyclones,  as  expounded  by  Clayton  or  by  Bjerknes  and 
Arrhenius,  nor  are  there  purely  dynamic  vortices  in  a  rapid 
stream  as  supposed  by  Hann,  nor  are  there  cyclonic  vortices 
caused  by  atmospheric  Islands  of  high  pressure  obstructing  a 
rapidly  flowing  eastward  drift  as  explained  by  Shaw,  or  by  Hil- 
debrandsson  in  his  report  to  the  International  Committee,  1905. 


ATMOSPHERIC  ELECTRICITY. 

By  GEORGE  C.  SIMPSON,  M.  S.,  Lecturer  in  meteorology  in  the  University  of  Manchester 
England.    Dated  January  17,  1906. 

The  study  of  meteorology  may  be  pursued  with  two  entirely 
different  ends  in  view.  We  may  pursue  it  for  utilitarian  pur- 
poses, or  we  may  pursue  it  as  a  pure  science  for  the  knowledge 
to  be  derived  from  it.  It  must  be  admitted  that  there  are  a 
number  of  so-called  meteorologists  whose  point  of  view  is  the 
former,  and  whose  highest  ambition  is  the  production  of  an 
almanac  giving  the  state  of  the  weather  for  each  day  a  year 
in  advance.  Although  some  of  the  great  advances  of  knowl- 
edge which  have  been  of  practical  use  to  mankind  have  been 
made  by  the  utilitarian  student,  yet  experience  has  shown 
that  without  the  pure  scientist  little  real  advance  can  be  made. 
The  true  men  of  research,  working  for  the  sake  of  science  itself, 
have  always  been  the  pioneers  to  open  up  new  country  and 
reveal  new  treasures,  which  the  utilitarian  has  then  appro- 
priated and  used.  In  meteorology  we  must  not  expect  and 
seek  for  merely  practical  knowledge,  but  must  investigate  the 
atmosphere  in  a  truly  scientific  manner,  considering  no  phe- 
nomenon found  in  it  to  be  unworthy  of  investigation.  Thus 
although  the  electrical  conditions  of  the  atmosphere  on  a  fine 
day  are  insignificant  in  comparison  with  the  great  motions  of 
the  atmosphere,  or  with  the  local  conditions  which  determine 
the  climate  and  weather  of  any  place,  yet  meteorology  can 
not  be  complete  without  a  true  knowledge  of  these  conditions. 
While  meteorologists  must  always  be  more  concerned  with 
the  great  changes  in  the  motion,  temperature,  pressure,  and 
humidity  of  the  air,  they  must  also  not  forget  that  electricity 
plays  an  important  part  in  natural  phenomena.  Since  the 
time  of  Franklin  great  progress  has  been  made  in  our  knowl- 
edge of  the  electrical  conditions  of  the  atmosphere,  but  so  far 
the  progress  has  led  to  no  utilitarian  results,  and  the  problems 
of  the  thunderstorm  are  not  yet  solved.  In  the  present  article 
an  attempt  is  made  to  sketch,  in  as  few  words  and  as  simply  as 
possible,  the  lines  along  which  research  has  traveled. 

One  of  the  first  lessons  we  learn  on  being  introduced  to  the 
science  of  electricity  is  that  a  positively  charged  body  placed 
between  two  others,  one  having  a  positive  and  the  other  a 
negative  charge,  will  tend  to  move  toward  the  latter.  This 
we  are  told  is  due  to  the  "  electrical  field  "  set  up  by  the  op- 
positely charged  bodies. 


The  experiments  of  Franklin  showed  that  such  an  electrical 
field  exists  in  the  atmosphere  during  thunderstorms.  Later 
observers  have  shown  that  not  only  during  thunderstorms, 
but  also  under  normal  circumstances,  there  is  an  electrical 
field  in  the  lower  atmosphere,  such  that  a  positively  charged 
body  would  be  attracted  toward  the  surface  of  the  earth.  The 
electrical  field  of  the  lower  atmosphere  points  to  the  perma- 
nent presence  of  a  layer  of  negative  electricity  on  the  surface 
of  the  earth  with  a  corresponding  positive  charge  somewhere 
above  the  surface,  but  exactly  where  this  positive  charge  is 
has  been  the  subject  of  much  controversy. 

For  a  long  time  it  was  thought  that  the  negative  charge  on 
the  earth  is  a  charge  left  there  when  the  earth  first  became  a 
separate  member  of  the  solar  system.  If  that  had  been  so 
then  the  corresponding  charge  of  positive  electricity  would  be 
somewhere  right  outside  the  earth  and  its  surrounding  at- 
mosphere, in  fact  somewhere  in  cosmical  space.  We  should 
thus  have  expected  an  electrical  field,  similar  to  that  found 
near  the  surface  of  the  earth,  extending  with  only  slightly  di- 
minished intensity  to  heights  much  greater  than  those  of  our 
atmosphere;  but  observations  made  in  balloons  have  proved 
most  conclusively  that  the  electrical  field  found  near  the  sur- 
face has  nearly  disappeared  at  a  height  of  four  and  one-half 
miles  (reached  by  Gerdien,  November  5,  1903).  This  means 
that  the  outside  positive  charge  corresponding  to  the  negative 
charge  on  the  surface  of  the  earth  is  not  outside  the  atmos- 
phere, but  is  distributed  through  the  lohole  mass  of  air  in  the  lower 
atmosphere. 

This  result  leads  us  to  consider  iinder  what  conditions  elec- 
tricity can  exist  in  the  atmosphere.  Until  1900  the  concep- 
tion was  firmly  held  by  physicists  that  the  air  of  the  atmos- 
phere in  its  normal  state  is  a  perfect  nonconductor  of  elec- 
tricity, and  that  if  a  charged  body,  perfectly  insulated,  were 
placed  in  air  quite  free  from  dust  the  charge  would  be  re- 
tained indefinitely.  That  such  a  body  never  does  permanently 
keep  its  charge  was  always  ascribed  to  the  presence  of  dust 
in  the  air.  It  was  supposed  that  particles  of  dust  coming  into 
contact  with  the  body  take  a  part  of  the  charge  and  are  then 
repelled,  and  that  thus  in  course  of  time  the  charge  is  in  this 
way  entirely  dissipated  on  to  the  dust  of  the  air.  But  in  1900 
Elster  and  Geitel  in  Germany  and  C.  T.  R.  Wilson  in  England 
showed  that  not  only  does  a  perfectly  insulated  body  in  per- 
fectly pure  air  lose  its  charge,  but  that  the  presence  of  dust 
diminishes  the  rate  of  loss  instead  of  increasing  it. 

Just  before  this  time  new  ideas  had  been  formed  as  to  what 
takes  place  during  the  discharge  of  electricity  through  gases. 
It  had  been  demonstrated  that  most,  if  not  all,  the  phenomena 
then  known  to  accompany  the  discharge  of  electricity  through 
gases  could  be  explained  by  assuming  that  an  electrically  neu- 
tral molecule  of  a  gas  can  be  split  up  into  two  other  molecules 
or  two  atoms,  each  of  which  carries  an  electrical  charge,  one 
negative  and  the  other  positive.  To  these  charged  molecules 
the  name  "  ion  "  had  been  given,  an  "  ion  "  being  understood 
to  be  any  small  material  particle,  generally  of  molecular  di- 
mensions, which  carries  a  charge  of  electricity. 

Elster,  Geitel,  and  Wilson  at  once  pressed  this  theory  into 
service  to  explain  the  results  of  their  experiments.  They  as- 
sumed that  a  small  proportion  of  the  molecules  of  ordinary 
air  are  always  being  split  up  into  ions.  Thus  when  a  charged 
body  is  introduced  into  air  the  electricity  on  it  attracts  ions 
of  the  opposite  sign  which  neutralize  the  charge,  or  in  other 
words  the  charge  is  dissipated.  Numerous  experiments  were 
made  to  prove  or  disprove  this  theory,  but  it  has  withstood 
all  the  tests  and  is  now  generally  accepted.  Elster  and  Geitel 
proceeded  to  work  out  in  full  the  bearings  of  this  new  theory 
on  the  problems  of  atmospheric  electricity.  It  at  once  be- 
came obvious  that  if  there  are  always  both  kinds  of  ions  in  the 
atmosphere  the  negative  charge  on  the  earth  will  attract  the 
positive  ions  toward  itself,  become  neutralized  and  so  disap- 


FEBRUARY,  190G. 


MONTHLY  WEATHER  REVIEW. 


74 


STUDIES  ON  THE  THERMODYNAMICS  OP  THE  ATMOS- 
PHERE. 

II.— COOKDINATION  OF  THE  VELOCITY,   TEMPERATURE,  AND 

PRESSURE  IN  THE  CYCLONES  AND  ANTICYCLONES 

OF   EUROPE   AND   NORTH   AMERICA. 

By  Prof.  FRANK  H.  BIGELOW. 

THE  ADOPTED  MEAN  TEMPERATURES  AND  GRADIENTS  ON  THE  1000-METER 
LEVELS  FOB  AMERICAN  AND  EUROPEAN  CYCLONES  AND  ANTICYCLONES. 

In  order  that  we  may  have  a  suitable  example  for  discussion 
in  the  application  of  the  thermodynamic  formulas  to  the  atmos- 
phere, it  will  be  profitable  to  adopt  an  average  system  of  tem- 
perature distributions  in  cyclones  and  anticyclones,  derived 
from  the  observations  that  have  been  made  available  by  the 
computations  of  the  preceding  paper  of  this  series.  The  prac- 
tical difficulty  of  securing,  by  numerous  ascensions  at  the  same 
time,  a  sufficiently  large  number  of  accurate  simultaneous 
observations  in  the  several  subareas  around  the  barometric 
centers,  for  all  the  levels  required  up  to  10,000  meters,  is  very 
great  when  one  special  temperature  disturbance  is  to  be  ob- 
served, as  in  an  individual  storm.  It  would  be  desirable  to 
make  numerous  simultaneous  ascensions  from  different  points 
of  the  same  cyclone,  as  has  been  done  in  Europe,  if  it  is  pos- 
sible to  do  so  from  many  stations,  say  for  25  to  40  in  number, 
but  the  result  will  then  be  to  give  the  conditions  in  only  one 
case,  and  it  would  of  course  require  many  similar  groups  of 
such  ascensions  to  enable  us  to  secure  what  may  be  accepted 
as  the  average  or  normal  type  of  cyclonic  temperature  distri- 
bution. Repeated  ascensions  at  a  single  station,  where  the 
facilities  for  the  work  are  generally  much  more  adequately 
elaborated,  accomplish  the  same  purpose  by  allowing  the  kites 
to  remain  aloft,  and  thus  permitting  the  cyclone  to  drift  past 
the  instruments  which  register  the  varying  changes  of  tempera- 
ture, pressure,  humidity,  and  wind  velocity.  By  utilizing  the 
numerous  ascensions  of  kites  and  balloons  made  at  Hald,  Ber- 
lin, and  Blue  Hill,  we  can  secure  the  approximate  normal  or  aver- 
age state  of  the  temperatures  with  which  to  explain  and  test  the 
proposed  thermodynamic  system.  Owing  to  the  incompleteness 
of  our  available  data,  it  is  necessary  to  assume  some  exten- 
sions of  the  probable  temperatures  beyond  the  actual  observa- 
tions, but  it  can  be  done  without  bringing  into  doubt  the  main 
principles  involved  in  this  discussion.  The  further  acquisi- 
tion of  observed  data  by  work  in  the  future  will  correct  any 
numerical  errors  that  may  now  arise  from  this  procedure.  In 
order  to  establish  the  theory  of  the  energy  of  storms  which  I 
have  proposed,  it  seems  proper  to  use  the  best  available  data 
in  these  preliminary  computations,  rather  than  wait  for  more 
completely  satisfactory  compilations  of  temperature  observa- 
tions. It  will,  also,  facilitate  a  correct  interpretation  of  the 
results  of  future  balloon  and  kite  ascensions,  if  we  can  show 
that  our  theory  is  capable  of  suitably  explaining  the  present 
adopted  mean  system  of  temperature  distributions  in  cyclones 
and  anticyclones.  We  can  infer  from  the  preceding  paper  that 
the  American  and  European  observations  at  the  three  given 
stations  in  the  lower  levels  approach  so  closely  together  in 
their  numerical  details  on  the  4000-meter  level,  that  we  shall  be 
justified  in  adopting  the  European  observations  above  4000 
meters  as  a  fair  representation  of  the  conditions  in  the  North 
American  atmosphere,  which,  however,  remains  to  be  practi- 
cally explored  in  the  higher  levels. 

In  order  to  concentrate  the  work  of  computation  which  will 
follow,  we  extract  from  Tables  1,  2,  3,  4,  the  temperatures,  T, 
in  centigrade  degrees,  for  the  several  1000-meter  levels,  as 
given  in  the  last  column  of  each  quadrant.  These  tempera- 
tures appear  in  the  left-hand  section  of  Tables  9  and  10,  which 
give  the  temperatures  and  variations  of  temperature  on  each 
1000-meter  level  in  American  and  European  cyclones  and  anti- 
cyclones for  the  winter  and  for  the  summer.  It  should  be 
noted  that  we  have  been  obliged  to  introduce  certain  values 
for  the  north  quadrant  in  the  American  data,  because  direct 


observations  are  entirely  lacking,  except  in  the  winter  high 
areas.  The  values  here  adopted  have  been  the  outcome  of  con- 
siderable labor,  and  they  may  be  found  to  need  some  modifi- 
cation as  the  result  of  other  direct  observations.  I  have  been 
guided  in  the  determination  of  the  interpolated  temperatures 
by  three  different  considerations,  (1)  the  relations  of  the  cen- 
ter areas  to  the  north  areas  in  general,  (2)  the  comparison  of 
the  European  data  with  the  American,  and  finally,  (3)  the  bal- 
ance of  the  entire  system,  consisting  of  the  four  sectors  of  the 
high  areas  and  the  four  sectors  of  the  low  areas  taken  in  con- 
nection with  the  mean  temperatures  and  gradients  of  the  atmos- 
phere without  regard  to  any  cyclonic  disturbances.  Thus, 
having  adopted  the  mean  temperatures  and  gradients  of  Table 
11  and  the  mean  variations  in  seven  sectors  of  Table  9,  it  is 
easy  to  compute  the  variation  in  any  missing  quadrant,  as  the 
north.  A  complete  balance  must  evidently  be  maintained, 
because  the  sum  of  the  excess  and  defect  of  the  temperatures 
in  the  several  areas  on  a  given  level  of  the  cyclone  and  anti- 
cyclone at  any  elevation,  as  1000  meters,  2000  meters,  etc., 
must  be  equal  to  zero.  However,  in  these  papers,  as  we  are 
concerned  only  with  approximate  relative  disturbances  of  the 
temperature,  and  since  individual  cyclonic  disturbances  differ 
widely  from  any  normal  type  that  may  be  adopted,  such  inter- 
polations may  be  admitted  for  the  purpose  of  discussion. 

TABLE  9. — Temperatures  and  variations  of  temperature  on  each  1000-meter 
level  in  American  cyclones  and  anticyclones. 

AMERICAN  WINTER  HIGH  AREAS.— From  Table  1. 


Height 

Temperatures  T. 

Means. 

Variations 

—AT. 

Mean 

meters. 

N. 

E. 

S. 

W. 

To- 

N. 

E. 

3. 

W. 

—AT. 

•  a 

0  a 

•G 

•o 

°C 

°C 

0  C.       ° 

a 

°C. 

°C 

6000 

—26.0 

5000 

19  5 

4000  .... 

—  7.9 

—18.8 

—17.9 

—  7.6 

—14.0 

+  6.1 

—  4.8    — 

3.9 

+  6. 

4 

3000..    .. 

—  3.9 

—12.7 

—12.6 

—  3.1 

—  9.0 

+  5.1 

—  3.7    — 

3.6 

+  5. 

9 

2000  .... 

-  1.2 

—  7.1 

—  8.3 

1.0 

—  4.8 

+  3.6 

—  2.3    — 

3.6 

+  5. 

8 

1000.      .. 

I.I 

—  3.5 

—  3.6 

4.5 

—  1.5 

+  3.3 

—  2.0    — 

2.1 

+  6. 

0 

0  ..    .. 

3.7 

2.0 

—  0.7 

9.0 

2.8 

+  0.9 

—  0.8    — 

».  » 

+  6. 

2 

AMERICAN  WINTER  LOW  AREAS. -From  Table  1. 


6000 

—26.0 

5000 

—19.5 

4000    . 

(-12.0 

—13.2    —18.7    —  1C.O 

-14.0 

+  2.0     +0.8     —  4.  7    —  2.0 

3.84 

3000    . 

-  7.0 

—  8.1     —12.6    —11.6 

-  9.0 

+  2.0     +0.9    —  3.  6    —  2.6 

3.43 

2000    . 

(-2.0 

—  3.  0    —  6.  3    —  7.  8 

—  4.8 

+  2.8    +1.8    —  1.5    —  3.0 

3.04 

1000    . 

-2.0 

—  2.  7    —  0.  1     —  6.  8 

—  1.5 

—  O.ft    -  1.2    +1.4    —  5.3 

2.73 

0    . 

(       2.0 

2.  8          6.  3    —  2.  7 

2.8 

—  0.  8          0.  0    +  3.  5    —  5.  5 

2.65 

/ 

Mean  

3.14 

AMERICAN  SUMMER  HIGH  AREAS.— From  Table  2. 


6000 

20.6 

5000 

—14.1 

4000  .... 

—  3.0 

—  8.4 

—  9.6 

—  4.8 

-  7.1 

+  4.1 

—  1.3 

—  2.5 

+  2.3 

3000  ...  . 

3.6 

0.1 

—  0.6 

2.0 

0.4 

\  3.2 

—  0.3 

—  1.0 

+  1.6 

2000  ..  . 

9.4 

7.1 

5.8 

8.1 

6.4 

+  3.0 

+  0.7 

—  0.6 

+  1.7 

1000  ...  . 

13.6 

13.0 

11.2 

12.1 

11.8 

+  1.8 

+  1.2 

-  0.6 

+  0.3 

0...  . 

17.9 

16.7 

14.5 

18.1 

17.2 

+  0.7 

-0.5 

—  2.7 

+  0.9 

AMERICAN  SUMMER  LOW  AREAS.— From  Table  2. 


6000 

—20.6 

—14.1 

4000 

-11.4 

—  6.0 

—  3.6 

—  9.0 

—  7.1 

-4.3 

+  1.1 

+  3.5 

—  1.9 

2.63 

3000 

—  1.4 

—  0.3 

3.1 

—  3.3 

0.4 

—  1.8 

—  0.7 

+  2.7 

—  3.7 

1.88 

2000 

4.  1 

4.8 

8.9 

3.0 

6.4 

—  2.3 

—  1.6 

+  2.5 

—  3.4 

1.98 

1000 

9.5 

10.2 

16.0 

8.8 

11.8 

—  2.3 

—  1.6 

+  4.2 

-3.0 

2.00 

0 

14.7 

15.6 

23.2 

16.9 

17.2 

—  2.5 

—  1.6 

+  6.0 

—  0.8 

1.53 

Me 

in  

2.00 

We  next  take  the  mean  temperatures  of  all  the  high  and 
low  areas  for  the  four  available  systems,  the  American  winter 
and  summer  up  to  4000  meters,  and  the  European  winter  and 
summer  up  to  about  10,000  meters,  and  set  them  in  the  middle 
column  of  Tables  9  and  10,  as  well  as  in  Table  11,  the  adopted 
mean  temperatures  and  gradients  on  the  1000-meter  levels  for 
American  and  European  cyclones  and  anticyclones.  It  will 
be  seen  that  at  the  4000-meter  level  the  temperatures  are 
almost  exactly  equal  in  the  two  regions,  for  winter  — 14.0° 


75 


MONTHLY  WEATHER  REVIEW. 


FEBRUARY,  1906 


TABLE  10. —  Temperatures  and  variation*  of  temperature  on  each  1000-meter 

level  in  European  cyclones  and  anticyclone*. 
EUROPEAN  WINTER  HIGH  AREAS.— From  Table  3. 


Heighl 

Temperatures  T. 

Means. 

Variations  —AT1. 

Mean 

in 
meters. 

N.          E.         8.          W. 

ft 

N.         E.          S.          W. 

—AT. 

0  C.        °  C        °  C.        °a 

°C. 

0  C.        °  C.        °  C.        °a 

°C. 

6000.. 

—27.0     -83.2    —24.5    -21.6 

—27.4 

+  0.  4    —  5.  8    +  2.  9    +  5.  8 

sum.. 

—19.4    —24.0    —18.3    —14.5 

—20.  4 

+  1.  0    —  8.  6     +  2.  1     +  5.  9 

4000.. 

—12.9    —18.0    -12.9    —  8.5 

—14.5 

+  1.  6    —  8.  5    +  1.  6     +  6.  0 

8000.. 

—  7.6    —13.  2    —  7.  9    —  3.  3 

—  9.0 

+  1.  4    —  4.  2    +  1.  1     +  5.  7 

2000.. 

-  2.  6    —  9.  0    —  6.  4         0.  8 

—  4.1 

+  1.6    —  4.9    —  1.8     +4.6 

1000.. 

0.  6    —  3.  8     —  2.  6          2.8 

0.8 

+  0.  8    —  4.  1    —  2.  9     +  2.  5 

0.. 

4.6          0.8          0.8          4.1 

4.3 

+  0.8    -3.5    —  3.  5    —  0.2 

EUROPEAN  WINTER  LOW  AREAS.-From  Table  3. 


6000. 

—26.5    —29.6    —27.8    —29.0  |  —27.4 

+  0.9    —  2.2    —  0.4    —  1.6 

2.50 

5000. 

—19.2    —22.4    —21.7    —23.8  i  —20.4 

+  1.2    —  2.0    —  1.3    —  3.4 

2.56 

4000. 

—13.0    —16.0    —15.4    —19.5     —14.5 

+  1.  5    —1.6    —  0.  9    —  5.  0 

2.70 

8000. 

—  6.6    —10.0     —10.0    —13.2 

—  9.0 

+  2.4    —  1.0    —  1.0    —  4.2 

2.63 

2000. 

—  1.8    —  5.0    —  4.2    —  6.6 

—  4.1 

+  2.  6    —  0.  9    —  0.  1     —  1.  4 

2.18 

1000.. 

2.1          1.0          1.4         0.5 

0.3 

+  1.8    +0.7    +1.1     +0.2 

1.70 

0.. 

6.9         4.2         6.6         6.5 

4.3 

+  2.  6    —  0.  1     +  2.  3    +  2.  2 

1.83 

Mean  from  0  to  4000  meters,  2.  21 

EUROPEAN  SUMMER  HIGH  AREAS.-From  Table  4. 


6000. 

-16.7 

—24.3 

-18.9 

—16.7 

5000. 

—10.6 

—17.2 

—13.1 

-10.2 

4000 

-  4.8 

—11.2 

—  7.7 

—  4.2 

3000. 

—  0.4 

—  6.6 

—  1.7 

0.8 

2000. 

2.7 

—  2.9 

2.6 

5.9 

1000 

6.8 

8.8 

7.4 

9.8 

0. 

18.7 

11.8 

12.8 

14.0 

—16.7 

—19.1 

+  2.4 

—  5.2 

+  0.2 

+  2.4 

-10.2 

-13.0 

+  2.4 

—  4.2 

—  0.1 

+  2.8 

—  4.2 

-  7.2 

+  2.4 

—  4.0 

—  0.5 

+  3.0 

0.8 

—  2.1 

+  1.7 

—  4.4 

+  0.4 

+  2.9 

5.9 

2.2 

+  0.5 

—  5.1 

+  0.4 

+  3.7 

9.8 

8.1 

—  1.8 

—  4.3 

—  0.7 

+  1.7 

14.0 

14.1 

—  0.4 

—  2.8 

-  1.8 

-  0.1 

EUROPEAN  SUMMER  LOW  AREAS.— From  TaWe  4. 


6000.. 

—18.8    —18.2    —21.9    -23.0 

—19.1 

+  6.  8     +  0.  9    —  2.  8    —  3.  9 

2.95 

MOO.. 

—  7.8    -11.6    —16.1    —17.1 

—13.0 

+  5.  2     +  1.  4    —  8.  1    —  4.  1 

2.91 

4000.. 

—  2.8    —6.9    —10.6    —10.6 

—  7.2 

+  4.4    +1.3    -  8.4    —  3.8 

2.79 

3000.. 

2.  0    -  0.  8    —  6.  9    —  4.  7 

-  2.1 

+  4.1     +1.8    —  3.8     —  2.6 

2.65 

2000.. 

6.4         4.2    -0.4    -0.9 

2.2 

+  4.2     +  2.0    —  2.6     —  3.1 

2.70 

1000.. 

12.6        12.0         5.7         6.7 

8.1 

+  4.  4    +8.  9    —  2.4    -1.4 

2.51 

0.. 

16.8        17.3        13.5        13.4 

11.  1 

+  2.7    +3.  2    —  0.6    —  0.7 

1.48 

Mean  from  0  to  4000  meters,  2.  43 

TABLE  11. — Adopted  mean  temperatures  and  gradients  on  the  1000-meter  levels 
for  American  and  European  cyclones  and  anticyclones. 


Height 
in 
meters. 

Winter. 

Summer. 

American. 

European. 

American. 

European. 

Ar 
~°        1000 

T        — 
•<o        1000 

AT 

T°      iooo 

T            AT 

iooo 

°a      °c. 

0  c.      '  a 

°  C         °  C. 

°c       °c 

16000 

—73.9 

—75.  4 

-72.  2 

-7l'.  1 

—3.5 

—3.5 

—4.0 

—3.0 

15000 

-70.4 

—71.9 

—68.2 

-68.1 

—3.0 

-3.0 

-8.0 

—2.5 

14000 

—67.4 

—68.9 

-65.2 

—65.6 

-2.5 

-2  5 

—3.0 

—2.5 

13000 

—64.9 

-66.4 

-62.2 

—63.1 

—2.0 

-2.0 

—4.0 

-4.0 

12000 

—619 

—64.4 

—68.2 

—59.1 

—4.0 

-4.0 

—5.5 

—5.5 

11000 

—58.9 

-60.4 

—52.7 

-53.6 

—5.5 

-5.5 

—6.0 

—6.5 

10000 

—53.4 

-54.9 

-46.7 

—47.1 

—6.6 

-6.5 

—6.7 

—7.0 

9000 

—46.9 

—48.4 

—40.0 

-40.1 

—7.1 

-7.0 

—7.0 

—7.5 

8000 

-39.8 

—41.4 

—33.0 

-32.6 

—7.0 

—7.0 

—6.5 

—7.0 

7000 

—82.8 

-34.4 

—26.5 

-25.6 

—6.8 

—7.0 

-6.9 

—6.5 

6000 

—26.0 

-27.4 

—20.6 

-19.1 

-6.5 

—7.0 

-6.6 

—6.1 

6000 

—19.5 

-20.4 

—14.1 

-13.0 

—6.5 

-5.9 

—7.0 

-5.8 

4000 

-14.0 

—14.5 

—  7.1 

—  7.2 

-6.0 

—5.5 

—7.5 

—5.1 

8000 

—  9.0 

—  9.0 

+  0.4 

—  2.1 

-4.7 

-4.9 

-6.0 

—4.3 

2000 

—  4.3 

—  4.1 

+  6.4 

+  2.2 

—2.8 

-4.4 

—6.4                            —5.9 

1000 

—  1.5 

+  0.8 

+  11.8                           +  8.1 

—4.3 

-4.0 

—5.4                              -6.0 

000 

+  2.8 

+  4.8 

+17.2                           +14.1 

and  —14.5°,  and  for  summer  —7.1°  and  —7.2°,  respectively, 
for  America  and  Europe.  This  indicates  that,  after  escaping 
from  the  confusion  in  the  circulation  near  the  surface,  about 


the  same  temperatures  prevail  in  the  midst  of  the  track  of  the 
cyclones  and  anticyclones  in  the  Northern  Hemisphere,  that 
is  over  Blue  Hill,  latitude  42°,  in  the  United  States,  and  over 
Hald,  latitude  56°,  and  Berlin,  latitude  52°,  in  Europe,  though 
the  stations  are  themselves  in  different  latitudes.  We  can, 
therefore,  admit  the  European  data  to  apply  to  the  American 
temperatures  above  the  4000-meter  level,  at  least  approxi- 
mately. 

I  have  also,  in  Table  11,  extended  the  temperatures  and 
gradients  up  to  16,000  meters,  using  the  known  temperatures 
derived  from  European  observations  so  far  as  possible  in  these 
high  elevations,  because  I  wish  to  secure  some  tentative  val- 
ues of  the  pressure,  the  density,  and  the  gas  factor  at  those 
altitudes,  to  be  computed  by  the  formula  which  will  be  intro- 
duced in  the  following  paper  of  this  series.  It  should  be  ob- 
served that  the  gradients  are  smaller  in  the  lower  levels  than 
in  the  middle  levels,  4000  to  10,000  meters,  and  that  they 
are  again  smaller  in  the  high  levels  above  10,000  meters. 
This  type  of  variation  in  the  gradients  conforms  to  the  warm 
zone  observed  by  Teisserenc  de  Bort  at  the  high  levels,  his 
"  isothermal  "  zone,  so  that  there  are  in  the  atmosphere  two 
zones  of  relatively  small  gradients,  the  lower  near  the  surface, 
from  0  to  4000  meters,  and  the  higher  above  10,000  meters. 
In  these  zones  there  are  rapid  alternations  in  temperature,  as 
compared  with  the  middle  zone,  showing  that  mixing  currents 
prevail  in  these  two  strata  of  the  atmosphere,  the  lower,  near  the 
surface,  being  the  region  where  the  cyclones  and  anticyclones 
are  generated  by  the  counterflow  of  warm  and  cold  currents, 
and  the  latter,  in  the  high  levels,  where  the  warm  air  over- 
flowing from  the  Tropics  mixes  with  cold  air  from  the  polar 
zones.  As  this  is  a  subject  belonging  to  the  general  circula- 
tion, further  discussion  of  it  will  be  postponed  to  a  later  paper. 
It  should  also  be  noted  that  I  have  gradually  eliminated  the 
annual  variation  in  the  temperature  in  the  levels  above  4000 
meters,  which  is,  I  suppose,  in  agreement  with  the  observed 
temperatures  in  the  high  levels.  These  adopted  data  will  at 
least  serve  as  examples,  approximate  to  the  truth,  for  intro- 
duction into  the  thermodynamic  discussions  to  follow. 

THE  VARIATIONS  OF  TEMPERATURE  IN  THE  SEVERAL  SECTORS  OF  CYCLONES 
AND  ANTICYCLONES  ON  EACH    1000-METEB  LEVEL. 

Having  derived  from  numerous  direct  observations  the  ap- 
proximate normal  temperatures  prevailing  in  typical  cyclones 
and  anticyclones,  I  proceed  to  deduce  a  somewhat  better  aver- 
age system  of  temperatures  by  the  following  discussion: 

If  T0  is  the  mean  or  undisturbed  temperature  which  pre- 
vails at  a  given  level,  independent  of  any  local  cyclonic  disturb- 
ance, and  T  the  temperature  at  a  given  disturbed  point,  as  in 
the  several  sectors  of  the  high  and  low  areas,  then  2'0=  T+  J  T, 
and  —  JT"=  T —  T0  is  the  correction  to  transpose  the  mean 
T0  into  the  observed  T.  Thus,  in  Table  9,  under  American 
winter  high  areas,  at  the  north  sector  of  the  4000-meter  level, 
the  temperature  is  — 7.9°,  which  is  +6.1°  warmer  than  the 
mean  temperature  of  that  level  — 14.0°,  taken  over  the  com- 
bined high  and  low  areas  of  the  region.  The  variations  AT 
of  the  second  section  of  Tables  9  and  10  are,  therefore,  the 
corrections  to  change  the  mean  T0  to  the  observed  temperature 
T,  in  which  the  sign  +  means  warmer,  and  the  sign  —  colder 
than  the  average  temperature  T0.  An  inspection  of  these 
tables  will  show  the  prevailing  temperature  variations  in  the 
several  quadrants,  and  a  comparison  of  the  American  with  the 
European  variations  up  to  4000  meters  shows  the  extent  to 
which  the  data  fail  to  conform  precisely.  Allowance  must,  of 
course,  be  made  for  the  fact  that  Blue  Hill  is  near  the  ocean 
on  the  eastern  side  of  a  great  continent,  and  Hald  and  Berlin 
on  the  northwestern  side  of  another  continent,  so  that  the  per- 
manent masses  of  air,  as  the  high  areas  to  the  northwest  of 
Blue  Hill  in  winter,  but  to  the  northeast  of  Hald  and  Berlin, 
or  the  high  area  to  the  southeast  of  Blue  Hill  in  summer,  and 
to  the  southwest  of  Hald  and  Berlin,  must  necessarily  make 


FEBRUARY,  1906 


MONTHLY  WEATHER  REVIEW. 


76 


differences  as  to  the  temperature  configurations  of  the  several 
quadrants  in  the  American  and  European  systems.  We  have 
been  proceeding  on  the  assumption  that  the  northern  sector  of 
the  cyclone  contains  the  "  saddle  "  of  pressure  described  in  my 
papers  on  the  barometric  distribution,  and  while  I  have  found 
it  actually  oriented  in  any  one  of  the  four  quadrants  at  different 
times,  yet  it  is  situated  to  the  north  of  the  center  in  the  great 
majority  of  instances  for  the  United  States. 

If  the  mean  variation  of  A  T  is  computed  up  to  4000  meters, 
without  regard  to  sign,  to  show  the  average  relative  distortion 
in  the  temperature  level  surfaces,  we  find  for  the — 

American    winter  areas,  the  mean  AT  =  3.14, 
American  summer  areas,  the  mean  AT  =  2.00, 
European   winter  areas,  the  mean  AT  =.  2.21, 
European  summer  areas,  the  mean  AT—  2.43. 
The  American  winter  disturbance  is  1.57  times  that  of  summer; 
the  European  winter  disturbance  is  0.91  time  that  of  the  sum- 
mer; the  American  winter  disturbance  is  1.42  times  that  of 
Europe;  and  the  American  summer  disturbance  is  0.82  time 
that  of  Europe.     On  the  whole  the  disturbances  of  tempera- 
ture were  about  the  same  in  each  of  these  districts  in  the 
weather  conditions  when   the   direct  observations   made    in 
balloon  and  kite  ascensions  were  executed.     What  the  relative 
values  are  in  more  strongly  developed  storms  remains  to  be 
determined  by  further  investigations. 

In  order  to  construct  the  mean  temperature  variations,  A  T, 
adopted  in  Table  12,  we  proceeded  as  follows:  The  variations 
of  Tables  9  and  10  were  plotted  on  diagrams  like  fig.  5,  the 
American  up  to  4000  meters,  the  European  up  to  6000  meters, 
and  then  lines  dividing  the  warm  areas  from  the  cold  areas 
were  drawn,  the  result  showing  that  there  is  a  similar  config- 
uration in  spite  of  minor  differences.  Then  the  mean  values 
of  these  two  systems  were  taken,  that  is,  the  arithmetical 
means  of  the  several  pairs  of  American  and  European  values 
in  the  same  sector,  so  that  the  two  observed  systems  were 
reduced  to  one  system,  which  made  another  drawing  like  fig.  5. 
The  sequence  of  the  numbers  in  the  same  sector  from  the 
ground  up  through  the  several  levels,  such  as  appear  in  Table 
12,  was  then  examined,  and,  on  the  assumption  that  the  change 
from  one  level  to  another  should  be  gradual,  and  in  harmony 
with  those  above  and  below,  it  was  possible  to  detect  imper- 
fections in  the  observational  data.  There  were  not  many  impor- 
tant changes  necessary  to  be  made,  and  the  final  changes  can 
be  checked  by  the  reader  from  Table  13,  which  is  the  adopted 
mean  system  taken  by  averaging  Tables  9  and  10,  together  with 
the  occasional  minor  corrections  mentioned.  These  gradient 
variations,  that  is,  the  AT  of  Table  12,  can  be  checked  in  the 
following  way:  The  sum  of  the  variations,  AT,  found  on  the 
same  level,  as  10,000,  9000,  etc.,  should  be  zero,  if  the  adjust- 
ments are  relatively  perfect.  An  examination  of  the  check 
sums  shows  that  they  conform  sufficiently  for  our  purposes,  as 
already  defined.  The  vertical  sequence  of  the  numbers  in  the 
several  sectors,  N.,  E.,  S.,  W.,  of  the  high  and  low  areas,  winter 
and  summer,  now  harmonizes  so  far  as  minor  irregularities  in 
our  observational  data  are  concerned,  but  it  will  be  proper  to 
modify  this  adopted  system  whenever  suitable  evidence  of  any 
important  inaccuracy  can  be  procured. 

We  may  observe  that,  generally,  the  north  and  west  sectors 
of  the  winter  high  areas  are  warm  throughout,  the  east  is  cool 
in  the  high,  and  warm  in  the  low,  while  an  inversion  of  tem- 
perature takes  place  in  the  south  sector.  The  last  sector,  to 
some  extent,  conforms  to  Professor  Hann's  inversion  data,  but 
the  other  sectors  do  not  confirm  his  view.  In  the  winter  low 
areas  the  north  and  east  sectors  are  warm,  the  west  is  cool, 
and  the  south  again  inverts.  In  the  summer  high  areas  the 
east  sector  is  cool,  the  west  is  warm,  and  the  north  is  warm 
up  to  7000  meters,  while  the  south  inverts  at  5000  meters  from 
cool  to  warm;  in  the  low  areas  the  north  and  east  sectors  are 
warm,  and  the  south  and  west  sectors  are  generally  cool. 


TABLE  12. — Adopted  mean  temperature  variations,  —  &T,in  American  and 
European  cyclones  and  anticyclones. 


WINTER. 


Height 
iu 
meters. 

Mean 
temperature. 

r0     —  AT 

High  areas. 
T—  T0  =  —  A3T 

Low  areas. 
T—  T0  =  —  AT 

Check 
sums. 

K.      E.      S.       W. 

N.       E.       S.       W. 

°  a       °c. 

°  C.     °C.    °C.    °C. 

°  a   o  a   °c.   °c. 

°  a    °  c. 

10000  

-54.2 

—1.0—2.0  +0.5  +2.0 

+2.2  +3.0  -2.0  -2.8 

+  7.  7  —  7.8 

—6.5 

9000..... 

—¥1.1 

—0.6  —2.6  +0.9  +2.4 

+2.0  +3.0  -2.2  -3.0 

+  8.  3  —  8.  2 

—7.1 

8000...   . 

—40.6 

+0.0  —8.0  +1.3  +3.0 

+1.6  +2.7  —2.5  —3.3 

+  8.  5  —  8.  8 

—7.0 

7000  

—33.6 

Q     Q 

+0.7  —3.5  +1.5  +4.0 

+1.2  +2.5  —2.6  —3.5 

+  9.  9  -  9.  6 

6000.  .  .. 

—26.7 

+1.4—1.0  +1.2  +5.0 

+1.1  +2.2  —2  8  —3.8 

+10.  9  —10.  6 

—6.7 

5000  

—20.0 

+2.0  —4.6      0.0  +5.7 

+  1.2  +2.0  —2.8  -4.0 

+10.9  —11.4 

—6.7 

4000  

—14.3 

+2.  8  —  4.  S  —1.  2  +6.  6 

+  1.8  +1.8  —2.4  —3.5 

+12.0  -11.4 

—5.3 

3000  

—  9.0 

+2.7  —4.0  —1.3  +4.8 

+2.2  +1.4  —2.3  —3.4 

+11.1  —11.0 

-4.8 

2000..... 

—  4.2 

+2.0  —3.8  —2.7  +4.0 

+2.4  +1.2  —1.3  —3.0 

+  9.  6  —10.  8 

—3.6 

1000  

—  0.6 

+1.5  —3.1  —2.5  +8.8 

+1.7  +1.3  +1.1  —2.2 

+  8.  9  —  7.  8 

—4.2 

0..... 

+  3.6 

+0.6  —2.1  —  as  +2.0 

+0.9  +1.1  +2.9  -1.7 

+  7.5  —  7.3 

SUMMER. 


10000  

^6.9 

—1.2  —1.5  +0.2  +1.0 

+4.8  +1.2  —2.0  —2.5 

+  7.2  -  7.2 

—6.8 

9000  

—40.1 

—0.6  —2.0  +0.5  +1.5 

+4.6  +1.2  —2.3  —2.8 

+  7.8  —  7.7 

—7.3 

8000  

—32.8 

—0.0  —2.5  +1.0  +1.8 

+4.4  +1.0  —2.7  —3.0 

+  8.2  —  8.2 

—6.7 

7000  

—26.1 

+0.7  —3.0  +1.5  +2.0 

+4.2  +1.2  -3.0  —3.2 

+  9.6  —  9.2 

-6.2 

6000  

—19.9 

+  1.4  —3.3  +1.2  +2.4 

+4.0  +1.4  —3.0  —3.5 

+10.  4  —  9.  8 

—6.3 

5000  

—13.6 

+1.9  —3.2  -0.1  +2.8 

+3.8  +1.4  —2.7  —3.0 

+  9.4  —  9.0 

—6.4 

4000  

—  7.2 

+2.8  —3.2  —0.5  +2.2 

+2.8  +1.8  —2.0  —2.6 

+  8.6  —  8.3 

—6.3 

3000..... 

—  0.9 

+  1.9  —2.9  —0.4  +2.0 

+2.  4  +0.  3  —1.  0  —2  6 

+  6.6  —  6.9 

—5.2 

2000  

+  4.3 

+  1.4  —2.2  —0.4  +1.6 

+  1.9  +0.2      0.0  —2.4 

+  5.  1  —  5.  0 

—6.7 

1000  

+10.0 

+0.5  —1.9  —1.2  +1.0 

+1.2  +0.4  +1.0  —2.2 

+  4.  1  —  5.  3 

—5.7 

0  

+15.7 

+0.2  —1.6  —2.0  +0.4 

+0.8  +0.8  +2.8  —1.5 

+  5.  0  —  5.  1 

These  facts  can  be  seen  plainly  on  tig.  5,  which  reproduces 
the  numbers  of  Table  12  in  a  graphic  form.  I  have  added  a 
few  arrows  to  suggest  the  probable  flow  of  the  cool  and  warm 
currents  in  the  several  levels.  Thus,  in  the  10,000-meter  level 
the  cool  current  is  from  the  northwest,  in  the  middle  levels, 
as  5000  meters,  from  the  north,  and  in  the  lower  levels  from 
the  northeast.  The  warm  current  is  generally  from  the  south 
with  a  smaller  rotation  from  the  southwest  through  the  south 
to  the  southeast.  I  should  like,  in  this  connection,  to  call 
special  attention  to  figs.  6  and  7  of  my  paper  III:  "The 
observed  circulation  of  the  atmosphere  in  the  high  and  low 
areas,"  MONTHLY  WEATHER  REVIEW,  March,  1902,  where  the  re- 
sults of  the  work  of  the  Weather  Bureau  on  the  circulation 
during  the  International  Cloud  Year,  1896-7,  were  summar- 
ized. The  observed  vectors  and  the  components  which  dis- 
turb the  normal  motion  of  the  atmosphere  are  there  given. 
Two  characteristic  features  were  then  marked  with  the  letter 
A,  one  on  the  northern  quadrants  of  the  cyclonic  components, 
and  the  other  on  the  southern  quadrants  of  the  anticyclonic 
components.  By  comparing  with  fig.  5  of  this  paper,  it  will  be 
seen  that  there  is  a  rotation  through  about  90°,  from  the  north- 
west to  the  northeast  in  the  north  quadrant,  both  for  velocity  compon- 
ents and  for  temperature  variations  in  passing  from  the  10,000- 
meter  levels  to  the  surface;  and  that  the  rotation  in  the  south  quad- 
rant is  less  in  the  respective  cases.  It  is  proper  to  infer  that  the  two 
systems  are  mutually  interdependent,  and  that  the  movement  of  the 
circulation  is  attended  by  a  corresponding  variation  in  the  tempera- 
ture distribution. 

At  the  time  of  constructing  the  chart  of  the  velocity  vec- 
tors, I  was  unable  to  explain  its  meaning,  and  as  it  differed 
radically  from  the  charts  of  velocity-motion  published  by  Mr. 


77 


MONTHLY  WEATHER  REVIEW. 


FEBRUARY,  1906 


Clayton  for  the  Blue  Hill  observations,  and  by  Professor 
Hildebrandsson  for  European  observations,  it  was  desirable 
that  some  criterion  should  be  found  which  would  indicate 
which  configuration  is  to  be  accepted.  My  charts,  as  there 
explained,  depended  upon  an  asymmetric  temperature  struc- 
ture of  the  cyclone  and  anticyclone,  while  the  Clayton-Hilde- 
braudsson  charts  seemed  to  favor  a  symmetrical  system,  such 
as  Ferrel  had  assumed  to  exist  in  his  theoretical  discussions. 
The  agreement,  however,  of  these  two  independent  sets  of 
observations,  velocity  vectors  by  the  Weather  Bureau,  and 
temperatures  by  Blue  Hill,  Hald  and  Berlin,  would  seem  to 
indicate  that  the  asymmetric  system  of  currents  must  be 
adopted.  While  I  can  not  claim  that  the  numerical  values  of 
Table  12,  and  fig.  6,  of  this  paper  are  entirely  correct,  it  yet 
seems  probable  that  the  prevailing  type  of  the  temperature 
configurations  in  the  several  levels  has  been  made  out  with 
sufficient  definiteness  to  permit  a  numerical  discussion  of  the 
data,  with  the  aid  of  the  thermodynamic  equations  in  connec- 
tion with  the  general  dynamic  equations  of  motion,  such  as 
will  be  attempted  in  the  other  papers  of  this  series. 

THE    MEAN    TEMPERATURE,     T,    IN    CYCLONES    AND    ANTICYCLONES. 

By  means  of  the  variations  of  temperature,  JT,  given  in 
Table  12,  using  the  mean  temperatures  of  the  second  column, 
we  can  find  the  mean  temperatures  in  each  sector,  N.,  E. ,  S., 
W.,  of  the  high  and  low  areas  for  summer  and  winter.  The 
result  is  given  in  Table  13,  mean  temperatures,  T,  in  cyclones 
and  anticyclones.  The  same  data  are  plotted  on  fig.  6, 
and  lines  dividing  the  warm  and  cold  areas  are  drawn,  which 
are  similar  to  those  in  fig.  5.  It  is  not  necessary  to  make  any 
extended  remarks  about  the  distribution  of  temperatures  at 
this  point,  but  the  relations  can  be  illustrated  by  fig.  7,  on 
which  the  temperatures  of  Table  13  are  suitably  plotted  for 
each  sector,  the  dotted  lines  standing  for  the  warm  areas  and 
the  full  lines  for  the  cool  areas.  The  scale  of  the  temperature 
abscissas  is  smaller  than  in  figs.  3  and  4  of  the  preceding  paper, 
in  order  to  extend  the  elevation  to  10,000  meters  instead  of 
6000  meters. 

From  Table  13  we  can  obtain  the  temperature  falls  in  1000 
meters  for  each  sector  by  subtracting  the  successive  tempera- 
tures, and  such  temperature  falls  per  1000  meters,  or  gra- 
dients, may  be  taken  as  the  true  average  for  the  middle  of  the 
stratum.  On  fig.  8,  marked  the  temperature  fall  per  1000 
meters  in  each  gradient,  these  results  are  plotted  at  the  middle 
distances  between  the  1000-meter  levels,  and  they  are  con- 
nected up  by  proper  curves,  which  form  an  interesting  study. 
The  first  remark  is  that  the  result  of  the  observations  in  the 
east  sector  of  the  high  levels  in  winter  and  summer  probably 
need  to  be  modified,  because  the  east  line  has  escaped  the 
concentration  common  to  all  the  other  lines.  The  second 
point  is  that  the  curvature  of  the  lines  indicates  the  prevailing 
cloud  strata;  that  is  where  the  lines  slope  upward  to  the  right, 
and  where  the  air  is  relatively  warmer  than  the  mean  gradient 
would  admit,  a  cloud  formation  takes  place,  as  cumulus  in  the 
1000-2000-meter  stratum,  cirrus  in  the  8000-10,000-meter 
stratum,  winter  and  summer,  and  alto-cumulus  in  the  4000- 
6000-meter  stratum  in  summer.  These  levels  contain  an 
especially  large  number  of  mixing  currents  of  warm  and  cold 
masses,  and  the  latent  heat  of  condensation  of  vapor  to  water 
adds  a  certain  amount  to  the  heat  transported  from  other 
regions.  The  third  and  most  important  remark  is  the  fact  that 
the  temperature  gradients  in  the  atmosphere  are  very  variable 
from  one  level  to  another,  and  that  they  are  always  smaller 
than  the  adiabatic  gradient,  9.87,  in  these  latitudes.  In  the 
latitudes  farther  south  and  in  the  Tropics,  at  least  in  the  lower 
strata,  the  adiabatic  gradient  is,  on  the  other  hand,  often  less 
than  that  actually  observed  in  the  atmosphere.  Such  relations 
of  observed  to  adiabatic  gradients  will  form  the  key  to  my  treat- 
ment of  the  thermodynamic  formulae  in  their  application  to 
the  atmosphere.  It  is  apparent  that  the  Ferrel  Canal  Theory 


of  the  general  circulation,  poleward  in  the  upper  strata  and 
equatorward  in  the  lower  strata,  must  be  practically  rejected  or 
greatly  modified  in  the  following  manner.  The  heat  energy  of 
the  Tropics  escapes  toward  the  poles  principally  in  two  strata, 
the  upper  in  the  cirrus  region,  where  there  is  mixing  with  cold 
currents  from  the  poles,  and  the  lower  in  the  cumulus  strata, 
where  there  is  also  mixing  with  the  cold  polar  streams,  while  be- 
tween these  layers  the  intermediate  strata  are  comparatively  free 
from  pronounced  intermingling.  The  exact  character  and  the 
extent  of  these  operations  in  the  cirrus  level  remain  to  be  more 
fully  investigated  by  suitable  observations,  which  are  re- 
quired before  the  needed  details  can  be  secured.  Especially  in 
the  tropical  zones  it  is  important  to  procure  accurate  thermal 
gradients  up  to  high  levels.  The  final  solution  of  the  problem 
of  the  circulation  of  the  atmosphere  is  dependent  upon  such 
an  exploration  of  the  temperature  conditions,  because  from 
these  data  alone  can  the  corresponding  pressure  and  density 
be  computed. 

TABLE  13. — Mean  temperatures,  T,  in  cyclones  and  anticyclones. 
WIN  TEE. 


Height 
in 
meters. 

Meau 
tempera- 
ture. 

To 

High  areas. 

Low  areas. 

N. 

E. 

8. 

W. 

N. 

E. 

S. 

W. 

10000 

•  a 

—54.2 

°C. 
—55.2 

°C. 
—56.2 

"0, 

-53.7 

°C. 
—52.2 

°C 
-52.0 

°a 

—51.2 

°c. 

-56.  2 

•G 

—57.0 

9000 

—47.7 

—48.2 

—50.2 

—46.8 

-45.  3 

—  1.5.7 

—44.7 

-^9.9 

—50.7 

8000 

—40.6 

—40.6 

—43.6 

—39.8 

—37.6 

—39.1 

-37.9 

-^3.1 

—43.9 

7000 

-33.6 

—32.9 

-87.1 

—32.1 

—29.6 

-32.4 

-31.1 

—36.2 

-37.1 

6000 

—26.7 

—25.8 

—30.7 

—25.5 

—21.7 

—25.6 

—24.5 

—29.  5 

—30.5 

5000 

-20.0 

—18.0 

—24.6 

—20.0 

—14.8 

—18.8 

—18.0 

—22.8 

—24.0 

4000 

-14.3 

—11.6 

—IK.  6 

—15.  5 

—  8.7 

—12.5 

—12.  5 

—1C.  7 

-17.8 

3000 

-  9.0 

—  6.3 

—13.0 

—10.3 

—  4.2 

—  6.8 

—  7.6 

—11.3 

—12.4 

2000 

—  4.2 

—  2.2 

-  8.0 

—  6.0 

-  0.2 

-  1.8 

—  3.0 

—  5.5 

—  7.2 

1000 

-0.6 

+  0.9 

—  3.7 

—  3.1 

+  2.7 

+  I.I 

+  0.7 

+  0.5 

—  2.8 

0 

+  3.6 

+  4.2 

+  1.5 

+  0.1 

+  6.6 

+  4.5 

+  4.7 

+  6.5      +1.9 

SUMMER. 


10000 

-46.9 

-48.1 

—48.4 

—  i6.  7 

—4.5.9 

—42.1 

^15.7 

—48.9 

—  «9.4 

9000 

—40.1 

-^10.  7 

—42.1 

—39.6 

—38.6 

—35.6 

—38.9 

—42.4 

—  12.9 

8000 

—32.8 

—32.8 

—35.3 

—31.8 

—31.0 

—28.4 

—31.8 

—35.5 

—35.8 

7000 

—26.1 

—25.4 

—29.1 

—24.6 

—24.1 

—21.9 

—24.9 

—29.1 

-29.3 

6000 

—19.9 

—18.5 

—23.2 

—18.7 

—17.5 

—15.9 

—18.5 

—22.9 

-23.4 

5000 

—13.6 

—11.7 

—16.8 

-13.7 

—10.8 

—10.3 

—12.2 

—16.3 

—16.6 

4000 

-  7.2 

-  4.9 

—10.4 

—  7.7 

-  5.0 

-  4.4 

—  5.9 

—  9.2 

—  9.8 

3000 

—  0.9 

+  1.0 

—  3.8 

—  1.3 

+  1.1 

+  1.5 

—  0.6 

—  1.9 

—  3.5 

2000 

+  4.3 

+  5.7 

+  2.1 

|    ;:.'.! 

+  5.9 

+  6.2 

+  4.5 

^  4.3 

+  1.9 

1000 

+10.0 

+  10.5 

+  8.1 

+  8.8 

+11.0 

+  11.2 

+10.4 

+  11.0 

+  7.8 

0 

+  15.7 

+  15.9 

+  14.1 

+  13J 

+16.1 

+  16.5 

+  16.5 

+  18.5 

+  14.2 

RESUME  OF  THE  TYPICAL  DISTRIBUTIONS  OF  THE  VELOCITY,  TEMPERATURE, 
AND  PRESSURE    IN    CYCLONES  AND    ANTICYCLONES. 

Having  described  the  typical  distribution  of  the  velocity  in 
the  local  circulations,  as  in  the  International  Cloud  Report, 
1898,  or  the  MONTHLY  WEATHER  REVIEW  for  March,  1902,  the 
pressure  distribution,  as  in  the  MONTHLY  WEATHER  REVIEW  for 
February,  1903,  and  the  temperature  in  this  paper,  it  will  be 
proper  to  summarize  the  results  schematically,  as  in  figs.  9  and 
10.  The  former  gives  the  resultants  of  the  general  circulation 
in  the  north  temperate  latitudes  plus  the  local  component  dis- 
turbances, and  the  latter  simply  the  components  by  themselves, 
separated  from  the  prevailing  eastward  drift.  In  fig.  9  the 
velocity  is  seen  to  diverge  more  and  more  from  the  eastward 
direction  in  the  higher  levels,  and  gradually  to  break  up  into 
the  well-known  cyclonic  and  anticyclouic  gyrations  in  the  lower 


XXXIV— 40. 


FIG.  8.— Temperature-fall  per  1000  Meters  in  Each  Quadrant.     (Latitude  +40°  to  +60°.) 


II 


CD 
<B 

a 
-1 


i 

02 
§ 

o 
-3 


a 
3 

a1 

o> 
H 


o 
o 

3 


3 

,0 

S 


ci 
O 

f 

ci 


Hi 


! 


a* 
I 


o 

I 


a 

I 

o 

o 

-r-t 

a 
o 


-e 

9 

o 

•a 


i 


01 

§ 

•43 


1 

•a 


o 
1-1 

15 


<0 

y>- 


I 


FEBRUARY,  1906. ' 


MONTHLY  WEATHER  REVIEW. 


78 


levels.  The  anticyclone  has  a  system  of  outward  components 
from  top  to  bottom,  and  the  cyclone  a  system  of  inward  com- 
ponents from  bottom  to  top,  but  in  neither  case  can  there  be 
any  true  inversion  in  the  type  of  the  system.  The  tempera- 
tures show  that  the  wave  motion  is  intensified  on  approaching 
the  surface,  as  the  strong  eastward  drift  is  gradually  dimin- 
ished in  the  lower  levels.  The  pressure,  on  descending  from 
one  level  to  the  other,  in  the  same  way  gradually  takes  on  the 
well-known  features  of  the  high  and  low  pressure  areas,  the 
high  areas  standing  with  the  "  saddle"  toward  the  south,  and 
the  low  areas  with  the  "  saddle  "  toward  the  north.  The  closed 
isobars  decrease  in  density  from  the  surface  upward,  and  dis- 
appear at  two  or  three  miles  above  the  ground,  being  depleted 
at  the  top  by  penetration  into  the  eastward  drift.  Whenever 
closed  isobars  occur  there  is  a  vertical  component  of  the 
circulation,  downward  in  anticyclones,  upward  in  cyclones. 
There  is  evidently  very  little  vertical  movement  in  the  upper 
levels  of  the  atmosphere,  where  the  isobars  are  mere  wavy 
lines,  unless  some  unobserved  closed  isobars  occur,  as  is  prob- 
ably the  case  in  the  development  of  hurricanes  in  the  Tropics. 
In  fig.  10  the  disturbing  components  are  given  for  the 
velocity,  temperature,  and  pressure.  In  the  velocity  of  the 
auticvclone  there  is  a  gradual  transition  of  the  known  outflow- 
ing structure  at  the  surface  into  a  simple  loop  in  the  upper 
levels,  the  orientation  being  changed  only  a  little;  in  the 


cyclone  the  inflowing  components  are  better  preserved  from 
the  surface  to  the  higher  levels,  but  there  is  a  distinct  rotation 
of  the  structure  through  about  one  quadrant.  The  tempera- 
tures show  the  maximum  disturbances  on  the  boundary  of  the 
high  and  low  areas,  with  a  distinct  rotation  of  both  the  cold 
and  warm  areas  through  one  quadrant.  The  pressure  dis- 
turbances consist  of  closed  isobars  gradually  diminishing  into 
loops  in  the  higher  levels  and  rotating  through  one  quadrant, 
especially  in  the  cyclone.  In  one  aspect  the  analytical  solu- 
tion of  this  dynamic  structure  is  simpler  than  that  demanded 
in  Ferrel's  or  in  Guldberg  and  Mohn's  adopted  types  of  vor- 
tices, but  it  is  certainly  different  from  either  of  them.  It  is  evi- 
dently necessary  to  distinguish  carefully  between  the  cyclonic 
system  proper  and  the  resultant  system  formed  by  its  combina- 
tion with  the  general  eastward  drift,  so  that  the  mathematical 
analysis  shall  not  deal  with  the  components  and  resultants 
indiscriminantly.  It  is  not  proper  to  appeal  to  observed 
resultant  motions  in  the  atmosphere  in  verification  of  a  theory 
applying  solely  to  the  components,  namely,  the  cyclonic  and 
anticyclonic  gyrations  as  examples  of  a  special  form  of  vortex. 
Having  thus  found  at  least  an  approximate  system  of  correlated 
velocities,  temperatures,  and  pressures  in  the  atmosphere,  it 
will  be  possible  to  approach  the  mathematical  analysis  of  the 
structure  with  some  prospect  of  a  satisfactory  solution. 


MARCH,  190G. 


MONTHLY  WEATHER  REVIEW. 


110 


STUDIES  ON  THE  THERMODYNAMICS  OF  THE  ATMOS- 
PHERE. 
By  Prof.  FRANK  H.  BIUKI.OW. 

III.— APPLICATION   OF   THE   THERMODYNAMIC   FORMULAE  TO 
THE  NONADIABATIC  ATMOSPHERE. 

THE    NONADIABATIC    ATMOSPHERE. 

In  the  preceding  papers  of  this  series  it  has  been  shown 
that  in  the  latitudes  of  the  temperate  zones  the  atmosphere 
is  not  arranged  in  such  a  way  that  the  thermal  gradients 
conform  to  the  adiabatic  rate  of  change  along  the  vertical, 

dT 
-  -3-  =  9. 867°  C.  per  1000  meters,  but  that  they  depart  from  that 

rate,  being  generally  much  less.  In  the  tropical  zones  the 
few  available  observations  indicate  that  in  the  lower  strata  the 
temperature  gradient  exceeds  that  amount,  or  is  equal  to  it. 
Thus  O.  L.  Fassig1  found  the  mean  of  four  ascents  at  Nassau, 
in  June-July,  1904,  to  be  28.3°  C.  at  the  surface  and  18.3°  C. 
at  1000  meters,  evidently  the  adiabatic  rate.  H.  Hergesell* 
found  for  16  ascents  on  the  Atlantic,  in  the  region  between  the 
African  coast,  the  Canaries,  and  the  Azores,  the  following 
temperatures:  , 


Height. 

T 

AT 

Meiers. 

°C. 

°c. 

5000 

(-10.0) 

—  8.5 

4000 

—  1.5 

-10.5 

3000 

9.0 

Adiabatic  gradient. 

—  9.0 

2000 

18.0 

-  8.4 

1000 

26.4 

+  3.4 

0 

23.0 

This  is  an  average  adiabatic  rate  from  the  lower  cloud  level 
to  5000  meters,  but  differs  widely  from  that  rate  from  the  sur- 
face to  1000  meters.  He  also  reports*  an  adiabatic  rate,  for 
the  ascensions  of  1905,  from  the  surface  to  1350  meters,  then 
a  zero  or  even  a  positive  temperature  gradient  to  3550  meters, 
above  that  a  rather  rapid  fall  to  13,000  meters,  and  higher 
still  in  the  atmosphere  a  slower  rate,  indicating  an  intrusion 
of  warm  air. 

As  the  result  of  my  kite  work  from  the  U.  S.  S.  Caesar,  over 
the  North  Atlantic  Ocean  between  Hampton  Roads  and  Gib- 
raltar, during  the  Spanish  Eclipse  Expedition,  I  found  the 
temperatures  as  follows,  for  the  dates  June  24,  26,  28,  29,  30, 
July  5,  and  September  22,  1905: 


Height. 

Mean  of  5 
ascents. 

Julyo. 

Sept.  22. 

Mrlfrx. 
1000 

°a 

16.9 

°C. 
7.9 

°C. 
15.6 

800 

17.1 

9.3 

17.9 

600 

17.6 

11.1 

18.5 

400 

18.5 

13.2 

14  6 

200 

19.6 

15.6 

17.8 

0 

22.1 

18.0 

20.9 

These  evidently  approximate  the  adiabatic  rate  on  July  5, 
but  depart  from  it  on  the  other  dates,  notably  on  September 
22,  when  the  kite  ran  through  a  warm  stratification,  probably 
blown  from  the  peninsula  of  Spain  over  the  ocean.  These 
examples  show  plainly  that  meteorologists  must  be  prepared 
to  discuss  the  problems  of  the  circulation  of  the  atmosphere 

1  Kite  flying  in  the  Tropics.   0.  L.  Fassig.    M.  W.  R.,  December,  1903. 

1  Sur  les  ascensions  de  cerfs- volant  executees  sur  la  M6diterranee  et 

sur  1'ocean  Atlantique 1904.  H.  Hergesell.  Note  in  Oomptes  Ren- 

dus,  Jan.  30,  1905. 

3  Die  Erforschung  der  freien  Atmosphare  fiber  dem  Atlantischen  Ocean 
1905.  H.  Hergesell.  Met.  Zeit.  November,  1905. 


whether  the  thermal  vertical  gradients  are  adiabatic  or  not, 
and  since  our  common  formulae  are  confined  to  the  adiabatic 
case,  it  is  an  important  study  to  learn  how  they  can  be  practi- 
cally modified  and  rendered  flexible  enough  to  meet  the 
actually  existing  conditions. 


FIG.  11. 

I  have  made  an  attempt  to  indicate  the  probable  arrange- 
ment of  the  isothermal  surfaces  in  the  earth's  atmosphere  by 
means  of  fig.  11.  In  the  tropical  zones  the  adiabatic  rate  pre- 
vails up  to  a  certain  height,  as  the  dotted  line,  and  above  that 
a  slower  rate.  In  the  temperate  zones  there  is  an  intrusion  of 
the  adiabatic  rate  into  the  lower  levels  and  a  mixing  area,  but 
generally  the  temperature-fall  is  less  than  the  adiabatic  rate, 
resulting  in  a  small  gradient  near  the  surface  and  up  to  3000 
meters,  a  more  rapid  fall  to  10,000  meters,  and  again  a  slower 
fall  due  to  a  second  intrusion  of  warm  air  from  the  Tropics. 
In  the  polar  zones  the  temperature  gradients  are  probably 
small,  the  air  being  generally  cold,  and  having  only  small 
changes  from  the  surface  upward.  These  suggested  iso- 
thermal lines  should  be  compared  with  the  circulation  de- 
scribed in  my  paper,  MONTHLY  WEATHER  REVIEW,  January,  1904, 
fig.  19,  where  the  results  of  this  intrusion  of  the  types  I 
and  II  between  the  temperate  and  the  tropical  zones  are  ex- 
plained. The  arrows  are  reproduced  on  tig.  11,  where  it  is 
seen  that  three  circuits  are  proposed  for  each  hemisphere;  (1) 


Ill 


MONTHLY  WEATHER  REVIEW. 


MARCH,  1906 


the  tropic,  circulating  anticlockwise;  (2)  the  temperate-tropic, 
circulating  clockwise;  and  (3)  the  temperature-polar,  circula- 
ting feebly  anticlockwise  for  the  Northern  Hemisphere.  In 
the  temperate  zones  the  local  cyclonic  and  anticyclonic  sys- 
tems represent  the  products  of  the  vertical  as  well  as  the 
horizontal  mixing  of  the  currents  of  air  derived  by  transpor- 
tation from  different  latitudes.  The  excess  of  heat  of  the 
Tropics,  producing  an  adiabatic  distribution  of  temperature 
in  their  lower  strata,  works  out  poleward  at  the  top  and  at 
the  bottom  by  irregular  streams,  which  produce  a  varying 
system  of  temperature  gradients  in  the  atmosphere  of  the 
temperate  zones,  standing  about  midway  in  value,  namely, 
5.0°  C.  per  1000  meters,  between  that  prevailing  in  the  Tropics, 
9.87°  C.  per  1000  meters,  and  that  probably  prevailing  in  the 
polar  zones,  as  2.0°  to  3.0°  C.  per  1000  meters.  The  inter- 
change,of  heat  between  the  Tropics  and  the  polar  zones  is 
by  means  of  these  three  more  or  less  irregular  circuits,  which 
produce  primarily  the  well-known  masses  of  permanent  high 
or  low  pressure  areas  standing  over  the  oceans  and  continents, 
and  secondarily  the  rapidly  migrating  cyclonic  gyrations  of 
the  temperate  zones.  We  shall  make  an  effort  to  approach 
our  study  of  this  complex  circulation  by  a  transformation  of 
the  thermodynamic  formulae  into  forms  which  will  be  suitable 
for  computations  in  the  actual  atmosphere,  as  distinguished 
from  an  adiabatic  but  fictitious  atmosphere,  which  has  com- 
monly been  discussed  by  meteorologists. 

DEVELOPMENT  OF  THE  THEBMODYNAMIC  FORMULA. 

In  the  formulae  derived  for  discussing  the  circulation  of  the 
atmosphere,  it  is  important  that  the  velocity  should  be  ex- 
pressed as  a  function  of  the  temperature  in  a  nonadiabatic 
atmosphere.  It  has  been  generally  the  custom  to  treat  the 
velocity  as  a  function  of  the  pressure  P,  the  density  p,  and  the 
gravity  g,  but  it  will  be  equally  valid  and  more  valuable  to 
make  it  a  function  of  the  temperature  T,  the  specific  heat  at  a 
constant  pressure  Gf,  and  the  gravity  g.  We  must  in  doing 
this  assume  the  applicability  of  two  physical  laws  in  the  atmos- 
phere. There  has  been  a  difficulty  in  connecting  the  results 
obtained  by  these  two  methods,  which  will  be  pointed  out  in 
this  paper  and  their  reconciliation  will  be  explained. 

I.     THE  FIBST  FOBM  OF  THE  BABOMETBIC  FORMULA. 

The  special  feature  of  this  formula  is  that  the  density  p  is 
eliminated  by  the  following  process:  Assume  the  Boyle-Gay- 
Lussac  law,  P=pBT,  and  the  pressure  law,  — dP=f>gdz, 


gral  mean  temperature  is, 


dP 


(1)     Then,  —  -p-  RT=  gdz 


Since 


'*r; 


(2) 


dP 


By  definition  P^B^,,  and  *£  =^f, 


for  the  standard  conditions,  we  have, 


so  that, 


(3) 


dB 


gdz,  for  common  logs. 


*»       /'o-™     Jo 

For  the  hypsometric  formula  the  gravity  g  is  computed  from 
the  standard  gravity  ga  by  the  factors,  (1  +  ?•)= (1  +  0.0026  cos  2^) 

for  latitude,  and  ('l  +  1.25  ^  =  (1  +  0.000000196)  h  for  altitude, 


\ 


snce  <7= 


In  integrating  for  an  atmosphere  composed  of  dry  and  moist 
air  between  the  heights  z^  and  z,  the  temperature  term  T,  which 
is  variable,  is  taken  as  the  mean  temperature  of  the  air  column 
the  moist  air  is  accounted  for  by  the  factor, 


T,  =  Tm,   and    »  =  (  1  +  0.3670  )  =  (1  +  ao). 

0        zc  ° 

We  must  pass  from  P*  =—  »  (l  +  1.25  h~h'\  to  logarithms, 
P        K  \  R    l 

log  ~°  =(1  +  .00157)  log  E"  =(l  +  ry)  log  B«  by  adding  the  fac- 


tor 

Finally, 


-.K=  18400, 


for  7?0=0.760  meter 

Pm=  13595.8 

/>„  =1.29305 

3f=0.43429 

Hence,  by  integration, 


(4)   -  fdB 
*J    jj 


B0  Pm 


in  the  meter-kilogram  system. 


°'378         = 


I       f* 
B]  =  I  gdz,  because, 


0.378 


If    ™°  =  K!  is  computed  as  a  new  barometric  constant,  and 
Tm  (1  +  0.378  *B  \  =  Tr,  the  virtual  temperature,  then, 

(6)  Kt  Tr  log  -jj  =  gm  (z  —  zc)  in  mechanical  units. 

I  have  computed  the  logarithmic  tables  91,  92,  93  of  the 
International  Cloud  Report,  1898,  in  such  a  form  that  the  dry 
air  temperature  term  m,  the  humidity  term  ftm,  and  the  gravity 
term  -fin,  are  kept  separate  from  each  other  in 

(7)  log  B0  =  log  H  +  m  —  mil  —  mr, 

for  the  sake  of  accurate  and  flexible  applications  in  all  possible 
meteorological  computations.  Auxiliary  tables  can  be  con- 
structed from  these  primary  tables  for  any  desired  applications, 
by  way  of  shortening  the  work  in  special  cases,  such  as  in 
numerous  reductions  to  any  selected  plane,  or  in  computing 
the  pressures  from  point  to  point  in  the  atmosphere,  using  as 
arguments  the  temperatures  and  humidities  observed  in  bal- 
loon or  kite  ascensions.  Especially,  they  can  be  used  to  com- 
pute the  dynamical  units  of  force,  or  work  required  to  pass 
from  point  to  point,  by  simply  extracting  (z  —  z0)  from  the 
tables,  wifh  the  temperature,  humidity,  and  pressure  as  the 
arguments  and  multiplying  (z  —  z0)  by  gm,  so  that 


(8) 


/dP  . 

T- *•<—•>' 


when  there  is  no   circulation   or  velocity  term,    \  (<l*  —  <?*„)• 
This  result  is  in  conformity  with  the  equation, 

—  dP  =  f>gdz, 
with  which  we  began  this  discussion. 

II.    THE  SECOND    FOBM   OF    THE    BAROMETRIC   FORMULA    IN    AN    ADIABATIC 

ATMOSPHERE. 

In  formula  (108«)   of   my  collection   in  the   International 
Cloud  Report  the  abnormal  form  for  dry  air  was  written: 

p        (T—8mh\™ 
(9)  p  =  (     '—^     )    ,  which  is 


B_ 
B. 


(f*  \  ft  ^ 

1  +  0.378  R\,  where  e  is  the  vapor  tension.      Hence,  the  inte-     where  —  ^r-  is  the  actual  vertical  gradient  of  temperature  and 


MARCH,  1906. 


MONTHLY  WEATHEK  EEVIEW. 


112 


the  exponent  is  undetermined.     We  acquire  from  the  observa-     of  the  same  type  which  will  admit  other  temperature  gradients, 

<tT  dT 

tions  a  vertical  gradient,  -  ™ ,  which  generally  differs  from       ~  ^>  in  a  quasi-adiabatic  atmosphere.     It  has  been  assumed 

,  „  that  there  was  no  addition  or  subtraction  of  heat  in  the  varia- 

the  adiabatic  gradient, -rf ,  and   seek   to    determine    the     tion  of  the  pressures  and  temperatures,  but  as  this  is  only  a 

special  case  it  will  be  proper  to  take  the  general  case,  where 

proper  value  of  the  exponent  m.  the  quantity  of  heat  dQ  is  added  or  subtracted,  besides  that 

From  my  formula  (73),  in  the  adiabatic  state  for  dQ  =  0,     acquired  or  lost  during  the  expansion  and  contraction  pro- 
dP  cesses.     Since  in  the  stratifications  of  the  atmosphere  by  cur- 

rents possessing  different  thermodynamic  properties,  there  is 
departure  from  the  adiabatic  state  by  the  term  dQ,  we  shall 
resume  the  full  equation  for  discussion. 
Fig.  12  will  make  our  treatment  clear. 


we  have  0  =  CpdT —  RT  -5  ,  in  mechanical  units. 

dP 
(W)   Hence,  -p-  = 


dP       C1   dT 

=       ~     >  and  integrating, 


(11) 


=log 


T 


(12)  Again,   -^  =  - 

a 

(13) 
(14) 


dz 


TS_  dz 

7  n     =  9  J  71 


a 


R 
dB 


T., 


an 


E 


„.-£,  and 

o 

Substituting  in  (10) 
Tfr.  Hence, 


Zo 


(15) 


C   j  BqPmda   1      C 

Jgdz  =  -    rgpr-jj- 


B 


'=]fdT, 


T 

* 


0. 


as  before.     Hence,  we  see  that  -£  supplies  the  constants  for 


FIG.  12.— The  relation  of  the  observed  to  the  adiabatic  gradient. 
Let  T0  =  the  initial  temperature  at  the  height  00 
Ta  =  adiabatic  temperature  at  the  height  z 
T  =  observed  temperature  at  the  height  z 

the  barometric  constant  K  in  the  adiabatic  case  only.     These     Then  the  adiabatic  gradient  is  a  =-  -?- =  -" -— -", 
substitutions,  (12),  (13),  can  be  verified  by  referring  to  the  dz          z—za 

formulae  of  Table  14.     It  is  well  known  that  the  use  of  the  dT       T. —  T 

and  the  observed  gradient  is,     a  =  —  -j-  =  —     — 

CL  Z  Z  ~ ~  Z. 

is  not  applicable  in  the  actual  atmos-     T    ,  , .       ,  .,  dTa      T0 —  Ta 

Let  the  ratio  of  these  gradients,  n  =   iT=   ^5 — /p- 

o 
Having  regard  to  the  adiabatic  thermodynamic  equation, 

(18)  0=CpdTa-d^ 


B 


formula  D  = 


k_ 
k-l 


'T 

Z0-\Ta 

phere,  except  to  give  what  is  called  by  von  Bezold  the  poten- 
tial temperature  T0,  corresponding  with  (R .  T)  when  reduced 
to  the  standard  pressure  50. 

Making  the  following  substitutions, 


we  observe  that  the  thermal  mass  passes  from 


to  (Taz) 


B        q  =  p     J^  =  B,  and  l-    C  d  T  =  Tm ,  we  have          bv  tbe  oblique  Path  marked,  T0  to  Tv  in  conformity  with  the 
//A  Tn  z  J  formulae  iust  discussed;  it  can  then  be  carried  from  the  point 


( 16 )     g  (z  -  z0 )  =  R  Tm  log  V  in  Naperian  logarithms,  and 


formulae  just  discussed;  it  can  then  be  carried  from  the  point 
Ta  to  the  point  T  at  the  same  level  z  by  changing  the  tempera- 
ture through  (T — Ta),  and  the  addition  of  the  heat 
Q=CP(  T-Ta). 


This  result  can  be  obtained  again  by  another  process. 

P 
Assume,  -  dP  =  +  g  p  dz,  and  p  = 


Q=Cp(T-Ta), 


Now  we  have, 
from  (18),  and  adding, 
we  obtain, 


Then, 


_  dP  =    ,    9  dz 

Tj  D       fJ~J 

'dz 


,  and  by  integrating, 


>-9_  Cdz  - 
~  RJ    T~ 


. 
R 


III.    THE  BAROMETRIC  FORMULA  IN  A  NONADIABATIC  ATMOSPHERE. 

In  the  preceding  case  it  has  been  assumed  that  the  temper- 
ature varies  witn  the  height  by  the  adiabatic  law,  which  is, 

—      "  =  '^  =  -         =  0.0098695  °C.,  so  that  the  temperatures 
dz         Up         r  0 

k 

''TXi^i 


(19) 
(20) 

(21) 

/oo\         rff)  __  (^  fi'p ^^ 

p ' 

Since  dTa=ndT,  we  have  dQ=Gp(dT-dTa)~CpdT-CpndT. 
Subtracting  this  value  of  dQ  from  equation  (22)  we  find, 


Q  =  Cp  (T—  T0)  —  CdP,       or  in  the  differential  form 
J    p 


(23) 


=  CpndT- 


dP 


in  a  quasi-adiabatic  form, 


p        [T\k-i 
of  the  formula}  of  section  II,  of  which  p  =  (  yf )  ls    "le 

representative,  must  have  this  relation.  Now  it  is  known 
that  this  formula  in  the  atmosphere  does  not  apply,  except  in 
occasional  instances,  and  we,  therefore,  shall  seek  a  formula 


which  is  true  in  a  stratum  where  n  is  constant,  that  is,  where 

dT 

the  gradient  —  -  —  is  not  changing. 
dz 


1       RT 
Substituting,      =  -5-  >  we  have, 


(24) 


and 


113 


MONTHLY  WEATHER  REVIEW. 

Groater.  Adiabatic. 


MARCH,  19<»fi 


Loss. 


9.87 
19.74 
Tn-  T=  19.74 


n=l  = 


9.87 


9.87 
71—  T=9.87 


n=2; 


9.87 
T94 


T,—  T=4.94 


9.87 


7'  -  T=0 


P  =  0  x  Pn  =  0 


11.5 


ra  £ 

P, 


1.73 

/TT  \ 

Tg/TiJ 


T          \   '  in  *>  /          7'  \    '•*  i 

* \  *•'  ^1     /      •*       \    * 

•9.877  ^o~  \  2' +4.94  7 

3.  46  6.  9 

r     \  /     r     \ 

T+  9.87y  "  \jr+ 4.947 


>„     /A00*-1 

0   ==  \Tj 


!"=! 


FIG.  13.— The  variations  of  the  ratio  n  —  2i». 


(25) 


(26) 


- 


R     T 


T 


-p, 

t 


so 


that, 


g 

T\Jia 


The  last  forms  are  found  as  follows: 


By  definition,  — 


dTa 


:  a<>  = 


the  ratio, 


dTa 

''  dT 


a° 
a 


g  dz 


Since 


k         C,, 
Ic—l  ~=  R  ' 


(27) 


k-l 


g  dz 
RdT' 


Our  formula,  therefore,  differs  from  the  adiabatic  formula 

k 
by  the  factor  n  in  the  exponent  with^.—^  •  This  ration  between 

the  adiabatic  and  observed  gradients,  depends  upon  the 
amount  of  heat  added  or  subtracted  from  an  adiabatic  atmos- 
phere to  produce  the  given  observed  atmosphere  within  the 
stratum  z  —  00  where  the  gradient  remains  a  constant.  We  can 
evidently  pass  from  one  stratum  to  an  adjoining  stratum  either 
continuously  by  changing  n  gradually,  or  discontinuously  by 
changing  n  abruptly.  The  ratio  n  is  a  new  variable  to 
be  introduced  into  the  thermodynamic  equations  in  their  ap- 
plication to  the  atmosphere,  so  that  all  the  standard  thermo- 
dynamic equations  and  discussions  become  available  with  this 
simple  modification.  Such  an  exposition  as  was  given  by  M. 
Margules  in  his  admirable  paper,  "  Uber  die  Energie  der 
Stiirme,"  which  is  limited  to  the  adiabatic  case,  may  be  modi- 
fied in  this  way  and  be  made  very  useful  in  practical  meteor- 
ology. It  is  rarely  the  case  that  computations  of  T0  to  T, 
from  one  level  to  another,  z0  to  z,  can  be  made  by  general 
dynamic  formulae,  but  they  must  usually  be  observed  with 
balloons  and  kites. 


can  range  between 


dT.      adiabatic  gradient 
Ihe  ratio,  n  =  -T™  =  -^— -    — 3— -  — 3^ — 7 , 
dT       observed  gradient 

the  limits  n  =  0  and  n  =  o> ;  for  n  =  1  the  gradient  is  adia- 
batic; for  n  <  1  the  cooling  is  more  rapid  than  in  the  adiabatic 
gradient,  as  in  summer  afternoons  when  the  ground  is  super- 
heated and  cumulus  clouds  are  forming;  for  n  >  1  the  cooling 
is  less  rapid  than  in  the  adiabatic  gradient,  as  generally  in  the 
temperate  and  polar  zones;  the  Tropics  probably  conform  to 
the  adiabatic  gradient  in  the  lower  strata  of  the  atmosphere. 


IV.        CONSTRUCTION  OF  THE  PRIMARY  DIFFERENTIAL  EQUATION. 

Under  the  assumption  that  n  is  variable  we  now  differentiate 
the  equation  with  the  variables  P,  T,  n, 


(28) 


P 

P,~\T. 
Passing  to  logarithms, 

P  k  IT 

(29)logp-=n/l,_1loj    ' 


T\  nk-i 


or  for  one  limit, 


(30)  log  P  =  n-j^^  log  T.         Differentiate, 

dP  k     dT          k  11 

( 31 )  p-  =  n  £—_ --j-  -y-  -(-  ^-— ^ log  Trfn.      Substitute  j,  =     7J 


dP 
f,RT 


k      dT 


n-  Substitute/?        -  = 


(  33  )       :>  -  =  n  Opd  T  +  Gp  T  log  Tdn.      In  common  logs  and  to  dz, 


for  the  vertical  direction. 


•j  rrt 


Again,  since  nCp-j    =  —  g  ,  by  this  substitution  we  have, 


<86> 


'-j-,         and  hence, 


(36)     dP=  —  pgdz  +  (>CpTlogTdn. 

We  see  then  that  the  effect  of  the  change  from  an  adiabatic 
atmosphere  to  any  other  gradient  is  accomplished  by  adding 
the  term  />CpTlog  Tdn. 

If  it  should  happen  that  besides  the  strictly  mechanical 
velocities  thus  indicated  there  is  a  further  expenditure  of  heat 
by  radiation,  it  would  be  necessary  to  add  the  special  term, 
Q0  —  Q,  making,  from  (33), 


(37)          -       =(Q0- 


nCp(T-  Tt) 


It  is  better  to  say  that  the  full  term  Cp  T  log  T  (n  —  n0)  has  a 
radiation  part,  (Q—  Q0),  and  a  velocity  part,  Cp  T  log  T(n—n0Y. 
The  factor  n,  due  to  an  addition  or  subtraction  of  heat  other 
than  by  adiabatic  expansion  and  contraction,  fully  accounts 
for  the  presence  of  a  nonadiabatic  gradient,  through  the  strati- 
fication of  the  layers  of  air  due  to  transportation  horizontally 
from  one  latitude  to  another,  or  generally  from  one  place  to 
another;  or  else  through  the  addition  or  subtraction  of  latent 
heat  in  the  condensation  of  aqueous  vapor  to  water,  or  by  the 


MARCH,  1906. 


MONTHLY  WEATHER  REVIEW. 


114 


vaporization  of  water  to  aqueous  vapor.  In  effect,  by  the 
practical  use  of  the  factor  n,  we  can  dispense  with  the  difficult 
computations  which  occur  in  making  an  allowance  for  the 
action  of  the  vapor  contents  of  the  atmosphere;  or,  on  the 
other  hand,  we  can  substitute  for  ?i  its  equivalent  in  terms  of 
such  other  computations  as  may  be  found  convenient  for  par- 
ticular purposes. 

•  The  corresponding  formulae  involving  P,  T,  R,  t>,  and  n,  in 
terms  of  the  temperature  T,  become, 


the  static  state  there  considered  to  the  circulating  state  here 
computed.     Since  we  have 

(  45 )         g  (2  —  z0)  =  —  Gp  n  ( T  —  T0),  it  follows  that 
(46)         i(9«_g'o)  =  _Cpriog  T(n-n0),torQ-Q0  =  0, 
so  that  the  circulation  can  be  computed  directly  in  terms  of 
T  and  (n  —  /?0).     This  proves  that  the  energy  of  circulation  is 
derived  from  the  difference  of  temperature  gradients  in  neigh- 
boring masses  of  air,  where  n — ?i0  is  not  equal  to  zero.     More- 
over, since  the  integral  of  gdz  around  a  closed  curve  is  zero, 


(38)  J-  =  (^Y    *5   logP-logP.+  nz^jflog  T-  log  T0).  s     C(gdz)  ds  =  0,  and  we  have  the  remaining, 

•*  •         \  -^  o/  u 


(39)    = 


T. 


V ^   log  ,- log  ,. +  ^(1087- log  r.).       (47)       -/^.*-/f  *+/<*.)*-/«*. 

,/  o    r  o  o 


(40)        - 


T. 


;   log  .R  =  log  R0  +  (n  -  1)  (log  T  -  log  T0). 

;   log  p  =  log  ptt  +  k  (log  P  -  log  P0). 

It  is  evident  that  R  is  not  constant  except  in  the  adiabatic 
system  for  n  =  1 ;  and  that  only  that  density  determined 
through  the  use  of  n  is  generally  valuable  in  the  atmosphere. 

V.    APPLICATION  TO  THE  GENERAL  EQUATIONS  OF  MOTION. 

We  will  now  make  the  connection  between  this  system  of 
equations  and  the  general  equations  of  motion  which  have 
been  employed  in  meteorology.  From  the  equations  (200)  of 
the  Cloud  Report,  we  have,  in  connection  with  the  differentia- 
tions of  equation  (37)  along  the  axes  x,  y,  z,  for  the  acceleration, 


dQ  dT 

dx  f     dx          p 

-  =  ~  +  sin  0  (2  +  w  v)  w  +  cos  6  (2  w  +  v)  u 

,  40  \         P  ™y  "* 

dQ  dT  dn 

=  dy"  '*dy~     Jf       °g      dy 

13P  dw  U*  . 


Multiplying  by  dx,  dy,  dz,  the  equations  for  work  are, 

QP                                                         uwdx 
—  =  udu  —  cos  0  (2  u>  +  v)  vdx  -) — 

=  &Q—Cpnd  T—  Gp  T  log  Tdn 


—       =  vdv  +  sin  8  (2  u>  -\-  v)  wdy  -f  cos  6  (2<«  -f  v)  udy 
=  fjQ_  CpndT—  Cp  T  log  Tdn 

—  =  wdw  —  sin  0  (2  to  -f  v)  vdz  —       •  dz  +  gdz 
=  dQ  _  Cpnd  T—  Cv  Tlog  Tdn. 

Since,  by  substituting  vdx  =  udy,  wdx  =  udz  and  wdy  =  vdz, 
the  terms  in  (2  u>  +  v),  the  angular  velocity  of  the  earth  and 
the  atmosphere  relative  to  it,  disappear  in  the  summation, 
they  represent  a  deflecting  force  at  right-angles  to  the  direc- 
tion of  motion  at  the  velocity  q,  which  does  not  modify  the 
circulation  but  only  the  path  of  motion.  The  integral,  there- 
fore, becomes  between  two  places, 


(44) 


/'o 


P 

: 

f 


This  is  the  equation  employed  by  Bjerknes  in  his  discussion 
of  the  circulation  of  the  atmosphere,  and  is  applicable  only  in 
closed  curves,  along  all  points  of  which  P,  p,  q,  or  qdq  must  be 
known  by  observations.  The  difficulty  of  securing  such  ob- 
served data  simultaneously  along  the  circuit  at  a  given  time 
is  so  great  that  this  special  case  of  the  general  equation  will 
seldom  be  serviceable.  In  ordinary  meteorology  it  is  required 
to  integrate  between  the  two  points,  as  in  the  same  horizontal 
plane,  or  in  a  vertical  direction.  Since  the  term  £  (9*  —  q'0) 
is  expressed  in  mechanical  measures  and  represents  work  done, 
then  it  may  be  taken  as  equivalent  to  \  (<f — <f^  =  9(z' — 2'<>)> 
so  that 

(48)  £  q'= g  z',  and  q'=  2  g  z'. 

The  circulation  is  therefore  always  equivalent  to  a  falling 
velocity  through  the  height  z',  which  may  be  computed. 

Furthermore,  since  Q — Q0  is  also  given  in  mechanical  units, 
it  may  be  taken  as  equivalent  to 

(49)  Q-  Q0=g  (z"-z".)t  so  that 

(50)  Q=gz" 

and  the  stored  up  energy  of  radiation  is  equivalent  to  a  verti- 
cal work. 

It  follows  from  these  considerations  that  we  obtain 


It  is  noted  that  the  term  for  the  circulation  \  (q'  —  q'a)  must  be 
added  to  the  equations  of  sections  I,  II,  III,  IV,  to  pass  from 


(51) 


,dn 


dq   _  d  Q  _ 
dx        dx 

d3=dQ-C.>nu*  -CPT  log  2"t" ,  in  longitude. 
dy        dy  dy  dy 

—  CpT\og  T$!L  in  vertical. 


dT 


—  G^Tloe  T      ,  in  latitude. 
dx 

,dn 


dq  =dQ 

1    j  j 


-, 


Since  P=  ft[>m  g0,  we  obtain  in  a  stratum  of  mean  p, 


(52) 


=  <      w-  Q'}-  Gp  n  (  T~  T°}  -  CpT  log  T 


~n°}  I 

J 


It  is  readily  perceived  that  the  introduction  of  the  factor  n 
and  the  correlation  of  the  pressure,  velocity,  gravity,  radiation, 
specific  heat,  temperature,  and  gradient,  in  this  double  equa- 
tion leads  to  an  innumerable  number  of  special  combinations, 
taken  in  connection  with  the  equations  of  thermodynamics. 
These  embrace  the  first  and  second  laws  of  thermodynamics, 
cyclic  processes,  the  entropy  S,  the  inner  energy  U,  the  ther- 
modynamic  potentials  (F.  <P);  the  adiabatic,  isodynamic,  iso- 
metric, isothermal  physical  processes;  differential  relations 
with  pairs  of  variables;  thermodynamic  surfaces  and  lines  in 
gases;  the  adiabatic,  isodynamic,  isenergetic,  and  isopiestic 
processes  with  other  variables  in  pairs;  the  gaseous,  liquid, 
and  solid  phases;  latent  and  specific  heat;  mixtures  and 
chemical  transformations,  chemical  dissociation,  their  solu- 
tions, and  other  relations,  involving  ionization,  electrical  and 
magnetic  fields  of  force.  This  vast  subject  is  open  to  mete- 
orological investigation  in  the  atmosphere,  and  will  no  doubt 
eventually  lead  to  important  practical  results. 


115 


MONTHLY  WEATHER  REVIEW. 


MAKCH,  1906 


VI.    FOUR    SYSTEMS    OF    CONSTANTS    FOR    THE    ATMOSPHERE. 

In  the  application  of  these  formulae  to  computations  of  ther- 
modynamic  and  dynamic  problems  in  the  atmosphere,  it  will 
be  convenient  to  have  for  ready  reference  a  table  of  the  most 
important  constants,  with  their  equivalents  in  the  four  systems 
of  units  likely  to  be  used.  Table  14  presents  such  a  compila- 
tion of  constants  in  the  following  systems  of  mechanical  or 
gravitational  units: 

1.  Meter-kilogram-second-centigrade  degrees. 

2.  Centimeter-gram-second-centigrade  degreen. 

3.  Meter-gram-second-centigrade  degrees. 

4.  Foot-pound-second-Fahrenheit  degrees. 

There  is  often  so  much  confusion  in  discussing  meteoro- 


logical problems  arising  from  the  use  of  now  one  system,  again 
another  system,  and  even  a  hybrid  system,  that  it  may  be  a 
check  against  errors  for  those  students  who  conform  to  the 
constants  here  given.  The  short  formulae  in  the  first  column 
define  the  quantities  with  precision,  and  the  numerous  trans- 
formations possible  among  them  give  rise  to  many  combi- 
nations such  as  occur  in  various  mathematical  discussions. 
Indeed,  it  is  surprising  to  note  how  large  an  amount  of  cur- 
rent meteorology,  occurring  in  treatises  and  analytical  papers, 
can  be  readily  reduced  to  these  elementary  formulae,  and  in 
reading  a  new  presentation  of  primary  principles  it  is  proper 
to  find  whether  they  conform  to  these  elementary  theorems 
or  not.  WTe  use  the  symbols: 


TABLE  14. — Mechanical  systems  of  constants  for  the  atmosphere  in  gravitational  units. 


Formulae. 

s. 

Meter-kilogram. 

Centimeter-gram. 

Meter-gram. 

Foot-pound. 

Psf^QQp  „.  B- 

00 

Log. 
9.  8060      0.  99149 

Log. 
980.  60      2.  99149 

Log. 
9.  8060      0.  99149 

Log. 
32.  172       1.50748 

Po 

13595.  8      4.  13340 

13.5958      1.13340 

13.5958      1.13340 

846.  728      2.  92774 

£„ 

0.760      9.88081 

76.  0      1.  88081 

0.760      9.88081 

2.  4934      0.  39680 

A 

101323.5      5.00571 

1013235.       6.  00571 

101.3235      2.00571 

67923.  5      4.  83202 

jQ==<7op{/0 

0o 

9.  8060      0.  99149 

980.60      2.99149 

9.  8060      0.  99149 

32.  172      1.  50748 

Po 

1.29305      0.11162 
7991.  04      3.  90260 

0.00129305      7.11162 
7991.  04      5.  90260 

0.00129305      7.11162 
7991.  04      3.  90260 

0.  080529      8.  90595 
26217.3      4.41859 

Po 

101323.5      5.00571 

1013235.       6.  00571 

101.  3235      2.  00571 

67923.  5      4.  83202 

/*(j—  /to  J(rf>o 

•Bo 

287.  0334      2.  45793 

2870334.       6.  4579S 

29.  2712      1.  46644 

1716.  43      3.  23463 

_J?Cp 

To 

273.       2.  43616 

273.       2.  43616 

273.       2.  43616 

491.  4      2.  69144 

00 

f,dh 
dT 

Po 

A 

1.  29305      0.  11162 
101323.  5      5.  00571 

0.00129305      7.11162 
101323.5      6.00571 

0.0012935      7.11162 
101.3235      2.00571 

0.  080529      8.  90595 
67923.  5      4.  83202 

*-*/* 

Po 

10332.  8      4.  01422 

1033.28      3.01422 

10.  3328      1.  01422 

2111.23      a  32454 

C^    k     lf>  ff 

It 

3.  461645      0.  53927 

3.  461545      0.  53927 

3.  461545      0.  53927 

3.  461545      0.  5392 

v     k  —  1  TO 

tc—l 

-    *    R 

t, 

7991.  04      3.  90260 

799104.       5.  90260 

7991.  04      3.  90260 

26217.  3      4.  4185 

t-1 

ffo 

9.  8060      0.  99149 

980.  60      2.  99149 

9.  8060      0.  99149 

32.  172       1.  50741 

—  SoPo 

t 

1 

1 

| 

1 

F 

2?3      7.56384 

273      7'56384 

273 

490      7'3085< 

=  —  go  dh 

<4 

993.  5787      2.  99720 

9935787.       6.  99720 

993.  5787      2.  99720 

5941.  57      3.  77391 

*0=£0. 

lo 

7991.  04      a  90260 

799104.       5.  90260 

7991.  04      3.  90260 

26217.8      4.4185 

-B  e 

0o 

9.  8060      0.  99149 

980.  60      2.  99149 

9.  8060      0.  99149 

32.  172       1.  5074 

^"  90 

1 

1 

1 

1 

1 

-    A 

278      7'56384 

273      7.56384 

273      7'86384 

490      7"'i085 

PO  r. 

-RO 

287.  0334      2.  45793 

2870334.       6.  45793 

287.  0334      2.  45793 

1716.43      3.2346. 

C^-R, 

c. 

706.  5453      2.  84914 

7065453.       6.  84914 

706.  5453      2.  84914 

4225.  14      3.  6258 

°p 

k 

1.4062486      0.14806 

1.  4062486      0.  14806 

1.  4062486      0.  14806 

1.  4062486      0.  14801 

c. 

t-1 

0.  40C2486      9.  60879 

0.  4062486      9.  60879 

0.  4062486      9.  60879 

0.4062486      9.6087 

t 

t^l 

3.  461545      0.  53927 

a  461M5      0.  53927 

a  461545      0.  53927 

3.461545      0.5392 

1 
l-l 

2.  461545      0.  39121 

2.461545      0.39121 

2.  461545      0.  39121 

2.  461545      0.  3912 

dT  go 
dk      C, 

dT 
~  dh 

0.0098695      7.99429 

0.  000098695      5.  99429 

0.  0098695      7.  99429 

0.  0054147      7.  7335 

1    ^go 

1 

4185.57      a  621  75 

41855700.       7.  62175 

4185.  57      3.  62175 

25027.  7      4.  3984 

A*       A 

2, 

A    -A 

Am  

0.0002389      6.37829 

2.389X10"8      2.37829 

0.0002389      6.37829 

0.  00003995      5.  6015 

0o 

e 

a  968      0.  59851 

I'r.  Th.   U. 

F 

1000.       3.00000 

100      2.00000 

1       0.00000 

367.  8      2.  56561 

A 

0.  002343      7.  36978 

2.343X10~6      5.36978 

0.  002343      7.  36978 

0.0012855      7.10901 

1 
A 

426.  837      2.  63022 

42683.  7      4.  63022 

426.  837      2.  63022 

777.  9      2.  8909 

MARCH,  1906. 


MONTHLY  WEATHER  REVIEW. 


116 


P0  =  pressure  in  units  of  force,  ga. 

pa   =  the  weight  of  a  given  mass  of  atmosphere,  pmBn  =  />0Z0. 

Cp  =  the  specific  heat  at  constant  pressure. 

Cv  =  the  specific  heat  at  constant  volume. 

G> 

j  rp 

—  -jj-  =  the  temperature  fall  per  unit  height  in  adiabatic  state. 

Ufl 

—r  =  the  mechanical  equivalent  of  heat,  426.8  and  777.9. 
A 

-^  =  the  factor  to  change  mechanical  units  to  heat  units. 
A 

F   =  the  factor  connecting  the  thermal  gradient  and  Pa. 
tt     =  the  number  of  British  thermal  units  in  1  kilogram- 
degree. 

VII.    THE  THERMODYNAMIC  CONSTANTS  FOR  THE  SUN. 

There  is  much  difficulty  in  passing  from  the  thermodynamic 
conditions  on  the  earth  to  the  corresponding  thermodynamic 
conditions  on  the  sun.  I  have  already  approached  this  sub- 
ject from  the  side  of  radiation  ill  my  "  Eclipse  Meteorology 
and  Allied  Problems,"  1902,  and  from  the  method  of  Nipher's 
Formulce,  in  my  studies  on  the  "Circulation  of  the  Atmos- 
pheres of  the  Sun  and  of  the  Earth,"  1904.  I  shall  briefly 
present  the  same  subject  as  the  immediate  development  of  the 
fundamental  formulae  introduced  in  this  paper.  It  is  not  so 
difficult  to  produce  a  self-consistent  system  of  quantities  as  it 
is  to  find  one  which  conforms  to  the  actual  physical  state  of 
the  sun,  and  I  conceive  that  it  is  proper  to  discuss  this  sub- 
ject in  several  ways. 

Specific  heat. 


(53) 


From  the  preceding  formula;,  we  have, 
dTgF  F  F 

dz 


_ga_ 
"(7.  " 


Hence, 


(54) 


ti" 


Since  f>,,J>n  =  /',/„  is  a  given  mass,  and  F  is  constant  for  a  given 
system  of  units,  it  follows  that  Cp  is  proportional  to  the  square 
of  the  gravity.  Taking  the  force  of  gravity  on  the  sun, 

( 55 )  (g)  ,un  =  gax  G  =  9.806  x  28.028  =  274.843 
it  follows  that  the  specific  heat  on  the  sun  is 

(56)  (Op)  sun  =  Cp  x  Gs=  993.5787  x  (28.028)'  =  780524. 

Adiabatic  rate  of  temperature-fall. 

( 57 )  For  the  earth  -  -  -3-  =  ^ -  =  9.8695°  per  1000  meters. 

dz       op 

/<m  gtG  _  9.8695° 

\  J,  I          —   7^732  —    9*. 


(58)     For  the  sun 


28.028 


=  0.32862°. 


Mechanical  equivalent  of  heat. 


j  rp 

( 59 )      From  —  -5-  =  -^f  for  the  earth,  we  have  on  the  sun, 


(60) 


dT 


—  -Qfa  =  £Tgi  •    Hence,  by  integration, 


(61) 

(62)  -< 

If  the  change  of  temperature  is  1°  then, 

is  the  mechanical  equivalent  of  heat,  and  is  obtained  by  the  fall 
of  a  mass  through  the  height  (z  —  z0)  G  under  the  force  of 
gravity  goG.  Whereas  on  the  earth, 

(64)  J-—  4185.57  =  426.8  x  9.8060,  we  have 

(65)  (M       =4185.57  x  (28.028) '  =  3288046. 

V*m/  sun 

Boyle-Gay-Lussac  Law. 
From  the  formulse  of  Table  14,  we  have, 

(66)  gl=P°=RT     =GpTk^±=_g      dh ^k-^^ 

on  the  earth,  and  we  infer  that  we  shall  have  on  the  sun, 


(67) 


(68) 
(69) 
(70) 

(71) 

., 
if 


dh 


Hence, 


10G'=  7991.04    x  (28.028)'. 

P,G'=  101323.5  x  (28.028)'. 

RG*=  287.0334  x  (28.028)'. 

X   28.028=7652°, 


ro(?=2730 


:  is  retained  a  constant  in  both  cases. 


k 

If  the  atmosphere  of  the  sun  is  composed  of  some  other 
material  than  />0  of  the  earth's  atmosphere,  then  the  proper 
modification  of  the  preceding  quantities  can  be  readily  com- 
puted from  terrestrial  data. 

Specific  heat  at  constant  volume. 

For  the  earth,  Gv  =  Gp  —  R,  and  hence,  for  the  sun, 

(72)  CVG'  =  CpG'  —  RG> 

(73)  (Cv)sun=  CVG*  =  706.5453  x  (28.028)'  =  555040. 


(  74)      Finally,  k  = 


=  1.4062486,  as  a  check. 


This  system  throws  the  entire  emphasis  upon  a  change  of 
gravity  depending  upon  the  mass  of  the  central  body,  rather 
than  upon  the  change  of  physical  conditions  implied  in  alter- 
ing the  ratio  of  the  specific  heats  k.  Since  the  temperature 
of  the  photosphere  may  in  this  way  be  taken  as  about  7652°,  and 
the  temperature  gradient  —  0.32862°  per  1000  meters,  it  follows 
that  the  effective  temperature  of  radiation  as  determined  by 
bolometer  measures,  6100°,  will  be  reached  at  the  height  of 
4418  kilometers,  or  2745  miles  above  the  surface  of  the  photo- 
sphere. This  change  of  1552°  may  be  sufficient  to  meet  the 
requirements  of  the  spectroscopic  observations  in  regard  to 
the  absorption  and  reversal  of  the  spectrum  lines.  The  gra- 
dient, —0.32862°  per  1000  meters,  is  28.028  times  greater  than 
that  obtained  by  my  other  methods,  the  difference  arising 
from  the  different  distribution  of  the  gravity  factor  G,  which 
seems  to  be  fully  accounted  for  in  these  formulae. 


JUNE,  1906. 


MONTHLY  WEATHER  REVIEW. 


265 


STUDIES  ON  THE  THERMODYNAMICS  OP  THE  ATMOS- 

PHERE. 

By  Prof.  FRANK  H.  BIGELOW. 
IV.—  NUMERICAL  COMPUTATIONS  IN  THE  VEKTICAL  OKDINATE. 

THREE  GENERAL    THEORIES    REGARDING  THE    FORMATION  OP    CYCLONES 
AND    ANTICYCLONES. 

There  seem  to  be  only  three  important  general  theories 
regarding  the  formation  of  cyclones  and  anticyclones  in  the 
earth's  atmosphere,  which  may  be  referred  to  those  authors 
who  have  been  conspicuously  associated  with  their  mathe- 
matical developments:  (1)  Ferrel's  cold  center  and  warm  center 
cyclones  and  anticyclones;  (2)  Oberbeck's  symmetrical  central 
cyclones  and  anticyclones;  and  (3)  Bigelow's  asymmetric  cy- 
clones and  anticyclones.  In  my  International  Cloud  Report, 
1898,  I  reviewed  the  mathematical  analyses  of  the  first  and 
second  theories,  and  gave  my  reasons  for  thinking  that  they  are 
inconsistent  with  the  air  currents  as  mapped  out  by  the  cloud 
observations,  as  well  as  with  the  distribution  of  temperature 
found  in  the  lower  strata.  These  theories  start  with  the  sys- 
tems of  isobars  which  near  the  surface  are  distributed  sym- 
metrically about  a  central  axis,  and  they  assume  that  the  tem- 
peratures are  similarly  arranged,  which  is,  however,  not  the 
case,  as  we  know.  The  two  central  systems  have  their  origin 
in  the  fact  that  the  second  equation  of  motion  can  be  dis- 
cussed in  two  ways.  Thus,  in  the  case  of  no  friction,  k  =  0, 
the  equation 

dv 
0  =  -r:  +  (2  n  cos  0  +  v,)  u  +  k  v, 

can  be  integrated  by  introducing  the  idea  of  a  boundary  cyl- 
inder about  the  system  at  the  radial  distance  zwo,  whence  is 
derived, 


/2w'        \ 

•u  =  I  —  ,  —  Ijrttn  COS  6, 
\     o  / 


which  is  the  tangential  velocity  at  the  distance  w.  This  is 
Ferrel's  method  and  several  difficulties  regarding  it  are 
mentioned  on  page  615  of  the  Cloud  Report.  The  second 
equation  of  motion  can  be  given  another  form  retaining  the 
friction  term,  where  A  =  2  n  cos  6,  so  that, 
do  uv 

from  which  are  derived  two  solutions, 
c 


First 


X 


Second  - 


H  c 

k  m 


These  form  the  basis  of  the  theory  developed  by  Guldberg 
and  Mohn,  Sprung,  Oberbeck,  Pockels,  and  others.  My  specific 
objections  are  summarized  on  page  623  of  the  Cloud  Report. 

The  construction  of  a  better  theory  was  at  that  time  very  diffi- 
cult, for  two  reasons,  the  first,  that  it  involved  breaking  away 
from  the  large  mass  of  current  literature  in  meteorology,  and 
that  it  introduced  many  new  ideas  concerning  the  general  and 
the  local  circulations  of  the  atmosphere,  the  two  being  inti- 
mately bound  up  together;  the  second,  due  to  the  lack  of  definite 
pressure  and  temperature  observations  in  the  higher  strata  of 
the  atmosphere.  In  the  course  of  chapters  8  and  11  of  the 
Cloud  Report  the  leading  ideas  regarding  the  asymmetric 
cyclone  and  anticyclone  were  sketched  out,  and  a  fairly  clear 
idea  was  given  of  the  probable  truth  regarding  the  formation 
of  these  circulating  structures.  Since  that  time  the  Weather 
Bureau  has  secured  daily  pressure  maps  for  the  United  States 
on  the  three  planes,  sea  level,  3,500  feet,  and  10,000  feet, 
throughout  an  entire  year,  1903.  This  valuable  material  has 
been  carefully  studied,  and  a  report  presented  on  the  subject, 
with  a  summary  of  the  results  in  the  MONTHLY  WEATHER  RE- 


VIEW, May,  1904.  The  recent  publications  of  the  temperature 
observations,  made  during  balloon  and  kite  ascensions  in 
Europe  and  America,  have  in  some  degree  supplied  this  de- 
ficiency, and  we  are,  therefore,  now  trying  to  discuss  more 
definitely  the  entire  subject  by  means  of  these  several  data  — 
velocity,  temperature,  and  pressure  —  than  has  been  possible 
heretofore.  In  the  preceding  papers  of  this  series  we  have 
given  the  temperature  data  and  the  thermodynamic  formulae, 
and  in  this  paper  we  shall  confine  our  attention  to  formula 
(44)  in  the  vertical  ordinate. 

COMPARISON  OF  THE  NUMERICAL  RESULTS  OF  COMPUTATIONS  BY  FORMULA 
(38)  AND  THE  GENERAL  BAROMETRIC  FORMULA  OF  THE  CLOUD  RE- 
PORT (59). 

Since  we  have  introduced  a  new  system  of  formulae  for  the 
computation  of  the  pressures,  densities,  and  the  gas  factors, 
from  the  temperatures,  through  the  use  of  the  ratio  n,  the 
ratio  of  the  adiabatic  temperature  gradient  to  the  observed 
gradient,  it  will  be  desirable  to  compare  the  numerical  results 
by  some  examples,  showing  the  relation  of  the  thermodynamic 
formulae  to  the  well-known  barometric  formulae.  Formula  (59) 
can  be  written  as  follows  : 


log|. 

In  our  new  thermodynamic  formula  we  have  made  no  at- 
tempt to  refine  it  by  introducing  corrections  due  to  the  vapor 

term,  —  lt!_  -  ,  the  gravity  term,  ?  °,  nor  the  land-mass  term, 
B  9 

(  1  +  -  -  ).      It  is  evident  that   these  will    require   a 

\  .' 

small  change  in  the  value  of  n,  and  the  subject  is  worth  an 
investigation,  but  for  our  preliminary  studies  of  cyclones  and 
anticyclones  these  refinements  have  been  omitted.  We  retain, 
then,  simply 

z—  z0=18400  (1  +  .00367  0)  log  3>  .........  (II) 

B 


where    8  = 


»  —  273°,  the  mean  departure  of  the  tern- 


perature  of  the  air  column  from  zero  centigrade.     This  is  to 
be  compared  with  the  formula, 

'-  P  fi 

'-log  T0)  =  log  £  =  log  3», (I) 

Jr  n 


and  it  will  be  sufficient  to  show  that 


18400+67.5  0 


*-!••*.), 


The  examples  are  taken  at  random  with  sufficient  range  to 
test  the  formulae  severely.     The  observed  gradient  is  found 

r ITI 

,  per  1000  meters.    The  computation  is  given 


from  a  = 


2— z 


in  full  as  an  example  of  the  numerical  quantities  involved. 
While  the  agreement  in  the  logarithms  is  not  perfect,  the  dif- 
ferences I — II  are  small  for  so  great  ranges  of  temperature 
and  height  when  translated  into  millimeters  of  mercury.  If 
5o=  760.00  mm.  in  the  fifth  example,  for  the  difference  0.00084 
the  value  of  B  is  294.00  and  294.57,  respectively.  As  my  only 
purpose  is  to  illustrate  the  numerical  validity  of  the  n  formula, 
it  will  not  be  necessary  to  inquire  further  into  the  causes  of 
the  small  differences  between  I  and  II. 

COMPUTATION  OF    MEAN    VALUES   OF    Pa,  />„,    E^,    FROM   TO    ON    THE 
1000-METER  LEVELS. 

In  making  an  application  of  the  formula  (44), 


266 


MONTHLY  WEATHER  REVIEW. 


JUNE,  1906 


TABLE  15. — Comparison  of  the  formula. 


Formula  l=—n^r-1  (log  7-  log  TO) 

T 
To 
T-T0 

271.5 
275.8 
—  4.3 

253.5 
275.8 
—22.3 

259.0 
268.7 
—  9.7 

219.6 
253.5 
—33.9 

233.2 
271.5 

:i8.:i 

290.0 
273.0 
+17.0 

300.0 
280.0 
+20.0 

275.0 
300.0 
—25.0 

280.0 
310.0 
-30.0 

Adlabatlc. 
Observed. 

-9.  8695 
—4.30 

—4.46 

—1.85 

-6.78 

-5.47 

+4.25 

+4.00 

—5.00 

—5.00 

—  log  n 

k/k  —  1 

-0.  36082 
0.53927 

-0.344% 

-0.30855 

-0.  16306 

—0.25630 

0.36590 

0.  39223 

—0.  29532 

-0.  29532 

iogr 

log  T0 

log  r—  log  T0 
log  (log  r—  log  T0) 

2.  43377 
2.  44059 
—0.  00682 
-7.  83378 

2.40398 
2.44059 
—0.  03661 
-8.  56360 

2.41330 
2.  42927 
—  0.01596 
-8.20330 

2.  34163 
2.  40398 
-0.06235 
—8.  79484 

2.  36773 
2.  43377 
—0.06604 
—8.  81981 

2.46240 
2.4I161G 
0.  02624 
8.  418% 

2.47712 
2.44716 
0.029% 
8.  47654 

2.43933 
2.47712 
—0.  08779 
-8.57738 

2.  44716 
2.  49136 
—0.  04420 
-8.64542 

log  I 

8.73387 
0.05418 

9.  44783 
0.  28043 

9.05112 
0.  11249 

9.49717 
0.31417 

9.  61533 
0.  41246 

9.32413 
0.  21092 

9.40804 
0.25588 

9.41197 
0.  25821 

9.48001 
0.30200 

Formula 

II               Z~Z° 

18400  +  67.5  « 

r-L-To 
» 

Z-Z0 

67.59 
K 
JT+67.59 

273.65 

+0.65 
1000 
+     44 
18400 
18444 

264.65 

—8.35 
5000 
—  564 

17836 

263.85 

—9.15 
2000 
—  618 

17782 

236.55 

—36.45 
5000 
-  2460 

15940 

252.35 

-20.65 
7000 
—  1394 

17006 

281.5 

+  8.5 
4000 
+  674 

18974 

290.0 

+17.0 
5000 
+  1148 

19548 

287.6 

+14.5 
5000 
+  979 

19379 

295.0 

+22.0 
6000 
+  1488 

19886 

n 

0.05422 

0.28034 

0.11247 

0.  31368 

0.41162 

0.  21082 

0.25578          0.25801           0.30173 

i—  ii 

—.00004 

+.00009 

+.00002 

+  .00049 

+.00084 

+.00010 

+.00010         +.00020         +.00027 

to  the  earth's  atmosphere,  it  is  evident  that  we  must  first  com- 
pute the  values  of  P0,  f>0,  -ff0,  corresponding  to  T0  as  observed 
in  the  air  while  it  is  undisturbed  by  the  local  cyclonic  and 
anticyclonic  circulations.  The  observations  of  temperature 
were  actually  made  in  the  midst  of  the  prevailing  local  disturb- 
ances, but  the  average  temperature  of  the  air  on  the  1000- 
meter  levels  was  found  by  taking  the  mean  temperatures  of 
the  eight  sectors,  four  in  the  high  areas  and  four  in  the  low 
areas,  as  in  Tables  10  and  11.  (See  MONTHLY  WEATHER  REVIEW, 
February,  1906,  Vol.  XXXIV,  p.  75.)  Thus,  Table  11  gives  the 
adopted  mean  temperatures  and  gradients  on  the  1000-meter 
levels  for  American  and  European  cyclones  and  anticyclones, 
and  these  data  are  used  in  the  following  computations. 

The  values  of  n  are  found  on  dividing  9.8695  by  the  gradient 
per  1000  meters,  assuming  that  the  gradient  is  a  constant  be- 
tween the  two  levels.  In  a  later  section  we  shall  compute, 
also,  the  values  of  n  on  the  1000-meter  levels  themselves,  taking 
as  the  gradients  those  found  on  fig.  8  at  the  points  indicated. 
We  use  the  mean  gradient  between  two  levels  in  computing 
P0,  |00,  jR0,  and  then  the  gradient  at  a  given  level  to  compute 
P,  p,  E,  the  abnormal  values  of  pressure,  density,  and  gas 
factor  produced  by  the  local  cyclonic  and  anticyclonic  dis- 
turbances. Having  found  n  from  level  to  level  the  following 
formula  are  applied  in  succession,  including  41  as  a  check: 


(38) 

(39) 
(40) 
(41) 


log  P  =  log  P0  + 
log  p  =  log  />„  + 


k 
k—L 


(log  T-  log  r.). 


k—1 


(log  T-  log 


log  R  =  log*.  +  (n— 1)  (log  T-  log 
log  p  =  log  Pt  +  I  (log  P  -  log  P.). 


A  special  point  should  be  noted  in  connection  with  the 
symbols.  P0  is  the  pressure  on  one  level,  as  the  1000-meter 
level,  and  then  P  is  the  pressure  on  another  level,  as  the  2000- 
meter  level,  corresponding  with  T0  and  T,  respectively.  In 
this  way  a  succession  of  values  of  P  is  found  in  the  several 
strata  of  the  undisturbed  atmosphere,  applying  to  the  gen- 
eral circulation  only.  In  studying  the  pressure  variations 
in  cyclones  and  anticyclones  these  P-pressures  become  P0  in 


formula  (44),  the  P-values  of  that  formula  referring  to  dis- 
turbances within  the  local  circulation  on  a  given  level.  I  have 
preferred  to  make  this  explanation  rather  than  complicate  the 
formulae  with  additional  symbols  for  all  contingencies.  In 
computing  the  tables  following,  the  pressure  P0  =  101323,  for 
B  =  760  mm.,  was  taken  as  the  initial  value.  The  initial  value 
of  the  density  on  the  sea-level  plane  was  computed  from, 


where  R0  =  287.0334,  and  T0is  the  value  from  Table  11,  T0  = 
275.8,  277.3,  290.2,  287.1.  While  it  is  true  that  the  atmosphere 
is  seldom  in  the  state  represented  by  these  tables,  yet  it  fluc- 
tuates about  these  mean  values,  just  as  it  does  about  the  mean 
pressure,  temperature,  and  density  at  sea  level,  and  it  is  con- 
venient to  have  reference  values  from  which  to  conduct  our 
discussions. 

TABLE  1G. —  Computed  values  of  the.  ratio  n 
between  successive  1000-meter  levels. 


Height 
in  meters. 

American. 

European. 

Winter. 

Summer. 

Winter. 

.Summer. 

16000 

3.037 

2.820 

3.037 

3.589 

14000 

4.886 

2.820 

4.386 

3.037 

12000 

2.078 

1.716 

2.078 

1.645 

10000 

1.518 

1.473 

1.518 

1.410 

9000 

1.390 

1.410 

1.410 

1.316 

8000 

1.410 

1.518 

1.410 

1.410 

7000 

1.  451 

1.678 

1.410 

1.518 

6000 

1.518 

1.518 

1.410 

1.618 

5000 

1.794 

1.410 

1.673 

1.702 

4000 

1.974 

1.316 

1.794 

1.936 

3000 

2.100 

1.653 

2.014 

2.295 

2000 

3.525 

1.828 

2.243 

1.673 

1000 

2.295 

1.828 

2.467 

1.645 

000 

JUNE,  1906. 


MONTHLY  WEATHER  KEVTEW. 


267 


_  q 

Since  n  =     T     T  ,  the  variation  of  n  in  Table  16  is  a  func- 

J      Jo 

tion  of  AT.  Where  AT  is  large,  n  is  small,  and  inversely. 
Hence,  in  the  lower  and  the  higher  levels  n  is  larger  than  in 
the  middle  levels,  the  change  of  temperature  being  slower 
below  and  above,  for  the  reasons  already  given.  In  the  middle 
levels  w  =  1.5  approximately,  and  it  may  become  twice  as  great 
in  higher  or  lower  strata.  Tables  17,  18,  19,  and  20  contain 


Computed  mean  values  of  the  pressure,  density,  and  gas  factor  from  the  tem- 
perature at  several  elevations. 

TABLE  19.— AMERICAN  WINTER. 


the  values  of  P0, 


Tf  on  the  several  levels,  and  their  loga- 


rithms which  are  useful  in  computations.     Since  Pa=g0pmBm, 
we  have 


B>1  ~  <7o  Pm  ~  9-806  X  13595.8  : 
The  pressure  is  higher  in  summer  than  in  winter  on  the  same 
level;  the  density  is  higher  in  winter  than  in  summer;  the 
gas  factor  is  higher  in  summer  than  in  winter;  and  the  tem- 
perature is  higher  in  summer  than  in  winter,  the  difference 
diminishing  in  the  upper  levels.  The  gas  factor  is  not  a  con- 
stant in  any  system  except  the  adiabatic,  where  n  =  1. 

COLLECTION  OF  THE  DATA  SHOWING  THE  DISTRIBUTION  OF    THE  DISTURB- 
ANCES ON  THE  1000-METER  LEVELS. 

We  will  collect  the  data  in  a  form  suitable  for  the  discus- 
sion of  the  distribution  of  the  energy  in  cyclones  and  anti- 
cyclones, leaving  the  reader  to  make  his  own  inferences  by  an 
examination  of  the  tables  in  their  relation  to  one  another. 

Computed  mean  values  of  the  pressure,  density,  and  gas  factor  from  the  tem- 
perature at  several  elevations. 

TABLE  17. -EUROPEAN  WINTER. 


Height 
in  meters. 

Po 

logPo 

PO 

logPo 

*o 

log  R0 

To 

log  TO 

16000  

9547 

3.  97987 

0.23733 

9.37535 

203.  59 

2.80874 

197.6 

2.  29579 

14000  

13414 

4.12756 

0.30226 

9.48038 

217.45 

2.33736 

2011 

2.30984 

12000 

18679 

4.  27135 

0.38250 

9.58263 

234.12 

2.  36943 

208.6 

2.31931 

10000  

25735 

4.41052 

0.48040 

9.68160 

245.63 

2.  39029 

218.1 

2.33866 

9000  

30097 

4.47753 

0.53610 

9.  72925 

249.  40 

2.39688 

224.6 

2.&5141 

8000  

34881 

4.54259 

0.59636 

9.  77551 

252.55 

2.40235 

231.6 

2.36474 

7000  

40335 

4.60569 

0.  66127 

9.82038 

255.65 

2.40765 

238.6 

2.  37767 

6000  

46450 

4.  66699 

0.  73108 

9.86397 

258.70 

2.  41280 

245.6 

2.39023 

5000  

53276 

4.72653 

0.80595 

9.90631 

261.70 

2.41780 

252.6 

2.40243 

4000  

60897 

4.  78461 

0.88636 

9.  94761 

265.80 

2.  42455 

258.5 

2.  41246 

3000  

69403 

4.84138 

0.  99536 

9.  98798 

270.  28 

2.  43181 

264.0 

2.42160 

2000  

78902 

4.  89709 

1.  06559 

0.  02759 

275.37 

2.  43991 

268.9 

2.  42959 

1000  

89502 

4.  95183 

1.16551 

0.  06652 

280.98 

2.  44867 

27&3 

2.  43664 

000  

101323 

5.  00571 

1.27300 

0.10483 

287.  03 

2.  45793 

277.3 

2.  44295 

TABLE  18.— EUROPEAN  SUMMER. 


16000  

10187 

4.00804 

0.24003 

9.38027 

210.20 

2.  32262 

201.9 

2.  30514 

14000  

14224 

4.  15302 

0.30434 

9.48336 

225.34 

2.35283 

207.4 

2.  31681 

12000  

19674 

4.  29388 

0.  38329 

9.58353 

239.% 

2.38013 

213.9 

2.33021 

10000  

26816 

4.  42888 

0.  47811 

9.  67953 

248.55 

2.  39542 

225.9 

2.35392 

9000  

31156 

4.  49355 

0.53152 

9.  72552 

251.68 

2.  40085 

232.9 

2.36717 

8000  

35994 

4.  55623 

0.58896 

9.77009 

254.21 

2.40520 

240.4 

2.38093 

7000  

41408 

4.  61709 

0.65069 

9.  81337 

267.22 

2.41031 

247.4 

2.  39340 

6000  

47453 

4.  67627 

0.  71690 

9.  85546 

260.70 

2.  41614 

253.9 

2.  40466 

5000  

54201 

4.73401 

0.78802 

9.  89654 

264.55 

2.  42241 

260.0 

2.  41497 

4000  

61730 

4.  79050 

0.86440 

9.  93671 

268.68 

2.42924 

265.8 

2.42455 

8000  

70118 

4.  84583 

0.94638 

9.  97606 

273.50 

2.436% 

270.9 

3.  43281 

2000  

79464 

4.  90017 

1.03443 

0.  01470 

279.14 

2.  44582 

275.2 

2.  43965 

1000  

89846 

4.95350 

1.  12882 

0.05262 

283.15 

2.  45202 

281.1 

2.44886 

000  

101323 

5.00571 

1.22956 

0.08975 

287.03 

2.45793 

287.1 

2.45803 

Height  in 
meters. 

Po 

l"g.Po 

Po 

logPo 

/?(, 

log  *o 

TO 

log  To 

16000 

9651 

3.98456 

0.24045 

9.  38103 

201.69 

2.30446 

199.1 

2  29907 

14000 

13527 

4.13120 

0.30571 

9.48531 

215.22 

2  ^289 

205.6 

2.31302 

12000 

18797 

4.27408 

0.  38630 

9.  58691 

231.60 

2.36497 

210.  1 

2  32243 

10000  .  .   . 

25833 

4.41217 

0.48430 

9.68511 

242.91 

2.38544 

219.6 

2  34163 

9000  
8000  

30114 
34915 

4.47876 
4.54338 

0.  54010 
0.  60037 

9.  73247 
9.77842 

246.61 
249.60 

2.39200 
2.39724 

226.1 
233.2 

2.35430 
2.  36773 

7000    .   . 

40369 

4.60605 

0.  66524 

9.82298 

252.64 

2.40250 

240.2 

2.38057 

6000  . 

46450 

4.  66699 

9.  73505 

9.  86632 

255.84 

2.  40797 

247.0 

2.  39270 

5000 

53251 

4.72633 

0.81006 

9.90852 

259.  31 

2.41382 

253.5 

2.40399 

4000 

60836 

4.  78416 

0.  89052 

9.  94964 

263.76 

2.42121 

259.0 

2.41330 

3000 

69321 

4.84087 

0.  97718 

9.98997 

268.71 

2.  42929 

264.0 

2,  42160 

2000 

78817 

4.89662 

1.  07059 

0.  02962 

273.  99 

2.43773 

268.7 

2.42927 

1000 

89440 

4.  95163 

1.  17127 

0.06866 

281.25 

2.44910 

271.5 

2.  43377 

000  

101323 

5.0D571 

1.27994 

0.10719 

287.03 

2.45793 

275.8 

2.44059 

TABLE  20.-AMERICAN  SUMMER. 


16000  

10232 

4.00995 

0.  23822 

9.37698 

213.88 

2.  33017 

200.8 

2.  30276 

14000  

14298 

4.  15529 

0.30223 

9.48033 

227.65 

2.35727 

207.8 

2.31765 

12000  

19754 

4.29565 

0.38031 

9.  58014 

241.79 

2.38344 

214.8 

2.33203 

10000  

26929 

4.43022 

0.  47407 

9.67584 

250.99 

2.39966 

226.3 

2.35468 

9000  

31252 

4.  49488 

0.52701 

9.  72182 

254.48 

2.40566 

233.0 

2.36736 

8000  

36107 

4.55759 

0.58401 

9.76642 

257.59 

2.41093 

240.0 

2.38021 

7500  

41554 

4.61861 

0.64537 

9.80981 

261.18 

2.  41694 

246.5 

2.  39182 

6000  

47652 

4.  67808 

0.  71138 

9.85210 

265.37 

2.42385 

252.4 

2.40209 

5000  

54449 

4.73599 

0.  78213 

9.  89328 

268.88 

2.42956 

258.9 

2.  41313 

4000  

62023 

4.  79255 

0.85802 

9.93350 

271.84 

2.43431 

265.9 

2.42472 

3000  

70402 

4.  84758 

0.  93892 

9.97263 

274.  24 

2.  43813 

273.4 

2.43680 

2000  

79712 

4.  90152 

1.02563 

0.01099 

278.  16 

2.44429 

279.4 

2.44623 

1000  

69968 

4.95409 

1.11782 

0.  04837 

282.60 

2.45117 

284.8 

2.45454 

000  

101323 

5.00571 

1.  21642 

0.08508 

287.03 

2.  45793 

290.2 

2.46270 

VALUES  OF  THE  TEMPERATURES   T,    TO  AND    T —  TO- 

The  temperature  data  given  in  Tables  12  and  13  (see 
MONTHLY  WEATHER  REVIEW,  February,  1906,  Vol.  XXXTV,  pp. 
76,  77)  have  been  reproduced  in  Tables  21,  22,  23,  and  24,  in  a 
form  more  convenient  for  carrying  on  the  computations  de- 
pending upon  them.  T  is  the  temperature  in  the  several  sec- 
tors; T0  is  the  mean  temperature  on  the  same  level  computed 
from  the  eight  sectors  of  the  correlative  high  and  low  areas; 
T  —  Ta  is  the  departure  of  the  disturbed  area  from  the  assumed 
mean  undisturbed  atmosphere  without  any  cyclonic  and  anti- 
cyclonic  action,  and  is  shown  on  figs.  5  and  6. 

VALUES  OF  THE  RATIOS  n,  n,  AND  (n  —  nj. 

These  are  the  ratios  on  the  several  1000-meter  levels,  and 
they  are  used  for  computing  the  energy  of  the  local  disturb- 
ances on  a  given  plane,  rather  than  in  reducing  the  elements 
from  one  plane  to  another,  as  was  required  for  constructing 
Tables  17, 18, 19,  and  20.  The  values  of  n  on  the  several  levels 
for  each  sector  were  scaled  from  fig.  8,  for  which  purpose  it 
was  constructed,  and  from  them  the  values  of  n  in  Tables  25, 
26,  27,  and  28  were  computed.  The  values  of  n0,  the  mean 
ratio,  were  found  by  taking  the  means  of  the  eight  values  of 
7i  in  the  sectors  on  the  given  plane.  Tables  25,  26,  27,  and  28 
contain  the  data  n,  na,  and  the  differences  n  —  na,  the  dis 
tribution  of  n  —  n0  being  given  in  fig.  14  on  the  several 

-9.8695. 
levels.     Since  «„  =     „,_  „,    is  a  certain  average  gradient,  if  n 


268 


MONTHLY  WEATHER  REVIEW. 


JUNE,  1906 


Values  of  T,  T0,  T—  T0  derived  from  Tables  1£,  IS. 
TABLE  21.— WINTEK  HIGH  AREAS. 


Distribution  of  the  values  of  n,  nc,  n  —  n0. 

TABLE  25.— WINTER  HIGH  AREAS. 


10000  

°c  °  a  °c.  °c. 

-55.2  —56.2  —68.7  -52.2 
—48.2  —60.2  —46.8  -48.  3 
—40.6  —48.6  —39.8  -37.6 
—82.9  —37.1  —32.1  —29.6 
—26.8  —80.7  —25.6  -21.7 
—18.0  —24.6  —20.0  —14.8 
—11.5  —18.6  —15.5  —8.7 
—  6.8  —18.0  —10.3  —4.2 
—  2.2  —  8.0  —  6.9  —  0.2 
+  0.9  -8.7  -  8.1  +  2.7 
+  4.  2  +  1.  5  +  0.  1  +  8.  6 

°C. 
-54.2 

—47.7 
—40.6 
—83.6 
—26.7 
-20.0 
—14.3 
-  9.0 
-  4.2 
—  0.6 
+  8.6 

0  C.         °  C        °  C          °  C.         10000 

1.607      1.778      1.574      1.835 
1.339      1.537      1.867      1.319 
1.282      1.495      1.348      1.246 
1.283      1.523      1.404      1.234 
1.323      1.567       1.613      1.272 
1.420      1.623      2.100      1.430 
1.747      1.725      2.317      1.974 
2.274      1.894      2.804      2.443 
2.920      2.285      2.937      3.056 
3.184      2.179      2.903      3.439 
2.991       1.769      2.467      3.290 

1.600 
1.444 
1.396 
1.403 
1.459 
1.602 
1.819 
2.105 
2.554 
2.661 
2.403 

-.093     +.178    —.026      —.065 
-.105     +.093    —.077      -.125 
—.114     +.099    —.048      —.180 
-.120     +.120     +.001       —.169 
-,136     +.108     +.154      —.187 
—.182     +.021     +.498      —.172 
-.072    —.094     +.498      +.156 
t.169    —.211     +.699      +.338 
+  866         269    +  383      +  502 

—1.0      -2.0      +0.5        +2.0 
9000    . 

9000  

-0.5      —2.5      +0.9        +2.4 
8000.. 

8000  

0.0      —3.0      +1.3        +3.0 

7000  

7000  

+0.7      -8.5      +1.8        +4.0 

0000  

6000  

+1.4       -4.0      +1.2        +5.0 
5000  

5000  

+2.0      -4.6         0.0        +5.7 
4000  

4000  

+2.8      —4.3      -1.2         +5.6 
3000  

8000        .  

+2.7      —4.0      —1.3        +4.8 
2000  

2000        

+2.0      —8.8      —2.7        +4.0 
1000  

+.528    —.482    +.242      +.778 
+.688    -.634     +.064      +.887 

1000          

+  1.5      —3.1      —2.5        +3.3 
000  

000  

+0.6      -2.1      —3.6        +2.0 

TABLE  26.-WINTER  LOW  AREAS. 

TABLE  22.-WINTER  LOW  AREAS. 

—82.0  —51.2  —66.2  —67.0 
—46.7  —44.7  —49.9  —80.7 
—39.1  —37.9  —48.1  —48.9 
—82.4  —81.1  —  «6.2  —37.1 
—25.6  —24.5  —29.6  —30.6 
—18.8  —18.0  —22.8  —24.0 
—12.6  —12.5  —16.7  —17.8 
—  6.8  —7.6  —11.3  —12.4 
—  1.8  —  8.0  —  6.5  —  7.2 
+  1.  1  +  0.  7  +  0.  5  —  2.  8 
+  4.5  +4.7  +6.  5  +1.9 

—54.2 
—47.7 
-40.6 
—33.6 
-26.7 
-20.0 
-14.8 
-  9.0 
—  4.2 
-0.6 
+  3.6 

1.687      1.547      1.613      1.659 
1.528      1.458      1.600      1.500 
1.471       1.447      1.437       1.443 
1.430      1.471      1.430      1.447 
1.426      1.518      1.458      1.498 
1.489      1.629      1.564      1.562 
1.629      1.766      1.707      1.690 
1.848      1.974      1.725      1.876 
2.903      2.518      1.667      2.150 
8.123      2.611      1.637      2.213 
2.632      2.367      1.643      2.065 

1.600 
1.444 
1.3% 
1.403 
1.459 
1.602 
1.819 
2.105 
2.554 
2.661 
2.403 

-.013    —.053    +  .013    +.059 
+.084    +.014    +  .056     +.056 
+.075     +.051     +  .041     +.047 
+  .027     +.068    +  .027     +.044 
—.033     +.059    —.001     +.039 
-.113     +.027     -  .038    —.040 
-.190    —.053    —  .112    —.129 
—.257    -.181    —.380    —.229 
+.847    —.0.%    —  .887    —.404 
+.462    —.050    —1.024    —.448 
+.229    —.036    —  .  758    —  .  338 

9000  

9000 

+2.0      +3.0      —2.2       —3.0 

7000          

7000 

+1.2      +2.5      -2.6        —3.5 

4000            

4000 

+1.8      +1.8      —2.4        —3.5 

TABLE  23.-SUMMER  HIGH  AREAS.                                                                                                TABLE  27.-SUMMER  HIGH  AREAS. 

10000 

-48.1  —48.4  —46.7  —46.9 
—40.7  —42.1  —39.6  —38.6 
—32.8  —85.3  -31.8  —81.0 
—26.4  —29.1  —24.6  —24.1 
—18.6  —23.2  —18.7  —17.5 
—11.7  -16.8  —18.7  —10.8 
—  4.9  —10.4  —  7.7  r  5.0 
+  1.0  —  3.8  -  1.8  +  1.1 
+  5.7  +2.1  +8.9  +5.9 
+10.5  +8.1  +8.8  +11.0 
+15.9  +14.1  +13.7  +16.1 

—46.9 
-40.1 
-32.8 
-26.1 
-19.9 
-18.6 
—  7.2 
—  0.9 
+  4.3 
+10.0 
+  15.7 

j  2          15      +0  2        +10       10000  

1.371      1.623      1.430      1.886 
1.233      1.482      1.307      1.328 
1.265      1.491       1.309      1.360 
1.392      1.662      1.537      1.469 
1.443      1.667      1.873      1.678 
1.447       1.589       1.905      1.725 
1.542      1.505      1.577       1.631 
l.!)47      1.569       1.645      1.818 
2.113      1.681       1.909       1.974 
1.905      1.637      1.974      1.909 
1.788      1.645      2.014      1.902 

1.603 
1.382 
1.396 
1.539 
1.628 
1.607 
1.563 
1.728 
1.869 
1.753 
1.688 

—.132    +.120    —.073      —.117 
.149     +.100        .076          .054 

8000 

00         25      +10        +18        8000  

—.131     +.095    —.087      -.036 
.147     +.123        .002          .070 

6000 

+14          83      +12        +2  4        6000  

—.185     +.039     +.245       +.045 
-.160    —.018     +.298      +.118 
-.021     -.058    +.014      +.068 
+.219     —.159    —.083       +.090 
+.244    —.188     +.040       +.105 
+.152    —.116     +.221      +.166 
+.097    —.043    +.326      +.214 

4000            .   . 

+2.3      -3.2      —0.5        +2.2        4OW  

TABLE  24.—  SUMMER  LOW  AREAS.                                                                                                   TABLE  28.—  SUMMER  LOW  AREAS. 

10000  

—42.1  —45.7  —48.9  —49.4 
-36.5  -88.9  -42.4  -42.9 
—28.4  —31.8  -36.5  —35.8 
—21.9  —24.9  -29.1  —29.3 
—15.9  —18.5  —22.9  —23.4 
—10.8  —12.2  —16.3  —16.6 
—  4.4  —  5.9  -  9.2  —  9.8 
+  1.6  —  0.6  —  1.9  —  3.5 
+  6.2  +  4.5  +4.3  +  1.9 
+  11.2  +10.4  +11.0  +  7.8 
+  16.5  +16.5  +18.5  +14.2 

-46.9 
—40.1 
32  8 

+4.8      +1.2      —2.0        —2  5       10000 

1.607      1.500      1.572      1.535 
1.443      1.394      1.445      1.422 
1.439      1.398      1.478      1.426 
1.559       1.516      1.597       1.582 
1.725      1.574      1.564      1.507 
1.744      1.569       1.430      1.447 
1.684      1.719      1.352      1.491 
1.769      1.943      1.386      1.744 
2.109      1.855      1.557       1.750 
1  974      1.673      1.384      1.572 
1.781       1.597       1.279       1.502 

1.508 
1.382 
1.396 
1.539 
1.628 
1.607 
1.563 
1.728 
1.  80!) 
1.753 
1.688 

+.104    —.008    +.069      +.032 
+.061     +.012    +.063      +.040 
+.043    +.002    +.082      +.030 
+.020    —.023     +.058      +.043 
+.097     -.054    —.064      —.121 
+  137         038          177           160 

9000  

+  4.6      +1.2      —2.3        —28        9000 

8000  

+4.4      +10         27           30        8000 

7000  

—26.1 
—19.9 
—13.6 
—  7.2 
-  0.9 
+  4.3 
+10.0 
+  15.7 

+4.2      +1.2      —30        —  32        7000. 

6000  

+4  0+14         30           35        6000 

{000  

+8  3      +14         27        3  0        5000 

4000  

+2  8      +13         20           26        4000 

+.121     +.156    —.211      -.072 
+.041     +.215    —.342       +.016 
+  .440    —.014    —.312      -.119 
+  .221     —.080    —.369      —.181 
+  .093    —.091     —.409      —.186 

8000  

+2  4       +0  3          10            26         3000 

2000  

+  19       +0  2          00            24         2000 

1000.              .... 

000  

+0.8      +0  8      +2.8           1  5          000 

JUNE,  1906. 


Distribution  of  the  heights  z  —  V     (z  —  sts)g  =  —Cfnv(T—T<>.) 
TABLE  29.—  WINTER  HIGH   AREAS. 


MONTHLY  WEATHER  REVIEW. 

Distribution  of  the  velocities  q,  q0,  J  (g* — g0*). 
TABLE  33. -WINTER  HIGH  AREAS. 


269 


Height 
in  meters. 

N. 

Cpn.,1 
E. 

T—  TO) 

S. 

W. 

a 

N. 

z  — 
E. 

*o 
S. 

W. 

10000     

1590 

3180 

—  795 

—3180 

9.786 

+162 

+325 

—  81 

—  325 

9000     

717 

3587 

—1291 

—3443 

9.789 

+  73 

+366 

—132 

—  352 

8000     

0 

4161 

—1803 

-4161 

9.791 

0 

+425 

—184 

—  423 

7000     

—  976 

4879 

—2091 

-5576 

9.793 

—100 

+498 

—213 

—  569 

6000    

—2030 

5799 

-1739 

—7248 

9.795 

—207 

+592 

—178 

—  740 

5000  

—3183 

7322 

0 

-9075 

9.796 

—325 

+748 

0 

—  926 

4000     

—5060 

7772 

2169 

-10121 

9.798 

—516 

+  798 

+221 

—1033 

3000  

—5647 

8.366 

2719 

-10039 

9.800 

-576 

+884 

+278 

—1024 

2000  

—5075 

9643 

6851 

-10150 

9.802 

-518 

+984 

+699 

—1036 

1000  

—3966 

8196 

6610 

—8725 

9.804 

^405 

+836 

+  674 

—  890 

000  

—1433 

5014 

8356 

—4775 

9.806 

—146 

+511 

+853 

—  487 

TABLE  30.—  WINTER  LOW  ABEAS. 


10000 

—3497 

—  4769 

3180 

4451 

9.786 

—357 

—487 

+325 

+454 

9000      

—2869 

—4304 

3156 

4304 

9.789 

-280 

—440 

+  322 

+440 

8000      

—2081 

—3745 

8468 

4577 

9.791 

—213 

—382 

+354 

+467 

7000     

—1673 

—3485 

3624 

4879 

9.793 

—171 

—356 

+870 

+498 

6000      

—1595 

-3189 

4059 

5509 

9.795 

-163 

-326 

+414 

+563 

5000    

—1910 

—3183 

4457 

6367 

9.7% 

—196 

—325 

+455 

+660 

4000  

-3253 

—3253 

4338 

6326 

9.798 

—332 

—332 

+448 

+646 

3000  

—1601 

—2928 

4810 

7111 

9.800 

—591 

—299 

+491 

+726 

2000   

—6090 

—3045 

3299 

7613 

9.802 

—621 

—311 

+337 

+  777 

1000  

—4495 

—3437 

—2908 

5817 

9.804 

—159 

-351 

—297 

+593 

000   

—2149 

—2626 

—6924 

4059 

9.806 

—219 

—268 

—706 

+414 

TABLE  31.—  SUMMER  HIGH  AREAS. 


0000 

1794 

2240 

—  299 

—1492 

9.786 

+183 

+229 

—  31 

—163 

9000 

824 

2746 

—  687 

—2060 

9.789 

+  84 

-t-280 

—  70 

—211 

8000 

0 

3468 

—1387 

—2497 

9.791 

o. 

+354 

—142 

—255 

7000 

1071 

4587 

—2294 

—3058 

9.793 

—109 

+468 

—234 

—312 

6000 

2265 

5338 

—1941 

—3882 

9.795 

—231 

+646 

—198 

—397 

5000 

3034 

5109 

160 

—4471 

9.796 

-312 

+522 

+  16 

—457 

4000 

3572 

4970 

777 

—3416 

9.798 

—364 

+607 

+  79 

—849 

3000 

—3262 

4979 

687 

—3434 

9.800 

—333 

+608 

+  70 

—350 

2000 

2600 

4085 

743 

—2971 

9.802 

—265 

+417 

+  76 

—803 

1000 

—  871 

3309 

2090 

—1742 

9.804 

—  88 

+338 

+213 

—178 

000 

—  669 

2683 

3354 

—  671 

9.806 

—  68 

+274 

+342 

—  68 

TABLE  32.-SUMMER  LOW  AREAS. 


0000 

7168 

—1792 

2987 

3733 

9.786 

—732 

—183 

+805 

+381 

9000 

—  6316 

—1648 

3158 

3845 

9.789 

—  645 

168 

+322 

+393 

8000 

6103 

—  1387 

3745 

4161 

9.791 

—623 

—142 

+382 

+425 

7000 

—6422 

—1835 

4587 

4893 

9  793 

—656 

—169 

+468 

+500 

6000 

—  6470 

—2265 

4864 

5661 

9.795 

—661 

—231 

+496 

+577 

5000            .     ... 

—5269 

—2236 

4311 

4790 

9.796 

—538 

—228 

+440 

+489 

4000 

—1348 

—2019 

3106 

4038 

9  798 

—444 

—207 

+317 

+412 

3000 

—  4120 

—  515 

1717 

4464 

9.800 

-420 

—  53 

+175 

+455 

2000  

—3528 

—  371 

0 

4457 

9.802 

—360 

—  38 

0 

+454 

1000  

—2090 

—  697 

—1742 

3832 

9.804 

—213 

—  71 

—178 

+390 

000  

—1342 

—1342 

—  46% 

2481 

9.806 

—137 

—137 

—479 

+253 

Height 
in  meters. 

N. 

E. 

9 

S. 

W. 

«o 
Mean. 

N. 

E. 

S. 

W. 

10000  

44 

39 

31 

34 

37.6 

+261 

+54 

—227 

127 

9000 

43 

38 

28 

38 

36  5 

+259 

+66 

274 

122 

8000  

41 

37 

26 

32 

85.0 

+228 

+  72 

—275 

—101 

7000  

39 

35 

23 

30 

32.9 

+220 

+72 

—277 

—  91 

6000  

37 

32 

20 

27 

29.9 

+238 

+65 

—247 

—  83 

5000 

34 

30 

17 

24 

26  9 

+216 

+88 

218 

74 

4000  

32 

28 

16 

23 

25.3 

+192 

+  72 

—192 

—  56 

3000 

30 

26 

14 

21 

23.6 

+172 

+60 

181 

58 

2000 

25 

20 

12 

18 

19.6 

+123 

+  10 

—118 

28 

1000  

19 

15 

10 

14 

14.8 

+  71 

+  3 

—  60 

—  12 

9 

9 

6 

7 

8.0 

+    8 

+  8 

—  14 

—    8 

TABLE  34.—  WINTER  LOW  AREAS. 


10000 

31 

35 

45 

42 

37.6 

—227 

—  95 

+306 

+175 

9000 

30 

33 

45 

42 

36.5 

—216 

—122 

+347 

+216 

8000 

28 

31 

44 

41 

35.0 

—221 

—132 

+356 

+228 

7000 

26 

29 

42 

39 

82.9 

—203 

—121 

+342 

+220 

6000 

23 

27 

38 

35 

29.9 

—183 

—  88 

+275 

+  166 

5000 

21 

25' 

34 

30 

26.9 

—142 

—  50 

+216 

+  88 

4000 

19 

24 

32 

28 

25.3 

—140 

—  32 

+192 

+  72 

3000 

18 

23 

30 

27 

23.6 

—117 

—  14 

+172 

+  86 

2000 

15 

18 

26 

22 

19.5 

—  78 

—  28 

+148 

+  62 

12 

13 

20 

16 

14  8 

38 

25 

+  96 

+  19 

000  

6 

7 

10 

10 

8.0 

—  16 

—  8 

+  18 

+  18 

TABLE  36.—  SUMMER  HIGH  AREAS. 


10000 

37 

33 

26 

29 

83.6 

+124 

—12 

—223 

—141 

9000 

35 

32 

24 

28 

32.5 

+120 

—16 

—240 

136 

8000.  

35 

31 

22 

27 

31.1 

+  129 

-  3 

—242 

—119 

7000  

33 

29 

19 

25 

29.0 

+124 

0 

—240 

—108 

6000 

31 

27 

17 

23 

26.5 

+130 

+14 

—207 

—  87 

5000  

29 

25 

14 

20 

23.9 

+185 

+27 

—188 

-  86 

4000  

27 

24 

13 

19 

22.4 

+114 

+37 

—166 

—  71 

3000  

25 

22 

12 

18 

21.0 

+  92 

+22 

—124 

—  59 

2000  

21 

17 

10 

15 

17.3 

+  71 

—  5 

—100 

—  37 

1000  

16 

12 

8 

12 

13.1 

+  42 

—14 

—  54 

—  14 

000  

8 

7 

5 

6 

7.3 

+  6 

-  2 

—  14 

—  9 

TABLE  S6.-SUMMEK  LOW  AREAS. 


10000      .  . 

29 

33 

42 

39 

33.5 

—141 

-17 

+321 

+200 

9000 

28 

31 

42 

39 

32.5 

—136 

—47 

+354 

+233 

ROOD 

26 

29 

41 

38 

31.1 

-146 

-63 

+357 

+239 

7000 

24 

27 

39 

36 

29.0 

—183 

—56 

+340 

+228 

6000 

21 

25 

35 

S3 

26.5 

—231 

—39 

+262 

+194 

5000     

20 

23 

32 

28 

23.9 

—  86 

—21 

+227 

+107 

4000 

18 

22 

30 

26 

22.4 

—  89 

—  9 

+  199 

+  87 

3000      .... 

17 

21 

28 

25 

21.0 

—  76 

0 

+  172 

+  92 

2000        

14 

17 

24 

20 

17.3 

-  52 

—  5 

+  139 

+  51 

1000    

11 

12 

19 

15 

13.1 

—  26 

—14 

+  95 

+  27 

000    

6 

7 

9 

9 

7.3 

—  9 

—  2 

+  14 

+  14 

270 


MONTHLY  WEATHER  REVIEW. 


JUNE,  1906 


Distribution  of  the  heat,  Q  —  §0,  and  the  pressure,  B  —  Ba. 
TABLE  37— WINTER  HIGH  AREAS. 


Height  in  meters. 

Q-% 

N.          E.          S.          W. 

B-Ba 
N.           E.          S.           W. 

10000             

—11.2+21.7—    8.8—    8.0 

—10.1  —  18.2  +    8.5     +  19.5 

9000           

—18.2  +  11.7  —    9.8  —  15.8 

—  5.7  —  22.8+    9.6     +23.4 

8000           

—14.9  +  13.0  —    6.4  —  19.7 

—  1.  1  —  80.  1  +  14.  7     +  32.  1 

7000         

—16.2  +  16.3  +    0.1  —  22.9 

+  7.1  —  89.5  +  19.2     t-  49.2 

6000       

—19.0  +  15.1  +  21.5  —  26.2 

+17.5  —  51.7  +  17.8    +  71.7 

6000     

—26.  3  +     3.  1   +  71.  9  —  24.  9 

+34.6—73.9+     1.3     +104.8 

4000       

—10.7  —  18.  9  +  73.9  +  23.0 

+60.1  —  75.4  —  23.6     +128.3 

3000           

+25.7  —  82.1  +106.0  +  51.4 

+69.1  —  94.8  —  80.6     +129.8 

2000     

+66.8  —  41.7  +  59.0  +  77.9 

+83.  2  —140.  0  —102.  1     +176.  9 

1000  

+82.6  —  76.0  +  88.1  +122.5 

+58.  1  —112.  7  —  91.  4     +137.  2 

000  

+94.4  —101.6  +  10.8  +142.5 

+15.  9  —  57.  1  —  92.  9     +  55.  6 

TABLE  38.— WINTER  LOW  AREAS. 


10000    

—  1.6    —  6.5  +     1.7    +7.2 

+  21.8    +12.0    —19.1    —25.6 

9000  

+10.6    —  1.8  +    7.1     +7.1 

+  19.9    +29.3    —21.3    —26.3 

8000  

+  9.8     +  6.6  +    5.6    +6.2 

+  16.8    +29.0    —26.4    —33.4 

7000  

+  8.6    +  9.  2  +    8.8    +6.0 

+  15.  2    +30.  6    —31.  1    —  40.  2 

6000  

—  4.  7    +  8.  2         0.  0    +  5.  5 

+  16.0    +30.9    —37.9    —49.8 

6000 

16.  4    +89  —    5.  6    —  5.  8 

+  21.  6    +36.  1    —46  9         57  3 

4000 

28.2          7.  9  —  16  6         91 

+  39  9     +39  2    —  50  6         70  7 

3000 

—  39  1        19  9        57.  7        34  8 

+  57  9    +35  9    —56  9    —  81  6 

2000 

+53  9         5.  6  —137  6    —  62.  7 

t!02  7     +53  9    —  51  9        113  3 

1000 

+72  8    —  79  —  161  2        70  6 

+  67.2    +61  0    +41  9         81  4 

000  

-f  36.  8    —  6.  8  —121.  5    —54.  3 

+  25.2    +30.4    +80.7    —46.0 

TABLE  39.— SUMMER  HIGH  AREAS. 


10000 

16  7    +15  2    —  98       14  8 

10  8        122+2.1      +94 

9000    

—19.5    +13.1    —9.9    —7.1 

—  6.0    —  17.9    +6.3      +14.5 

8000 

17  8    +12.9        11  8         50 

076        26  7    +11  8      +20  0 

7000 

20  6    +17  S         03         99 

-(-85    —  37  3     +20  8      +26  9 

6000 

26  7     +56    +35  4    +65 

+18  9        43  8    +17  9      +34.1 

6000  

—28.8    —2.8    +44.8    +17.6 

+26.6    —  43.6          03      +409 

4000  

—31.9    —  9.0    +  2.1     +10.4 

+33.  1        45.  0     —  6  6       +41  3 

3000  

+84.5    —26.0    —13.1     +14.2 

+34  6    —51.2    —  6  4      +37  5 

2000 

+  39  2        30  4    +  6  7     +16  9 

+32  2    —  49  3          84       +37  8 

1000 

+25  1        19  2    +36  5    +25  7 

+12.  7    —  48  2    —  30  3      +26  5 

000 

+16  4         72    +65  0     +36  2 

1    4.  5    •    36  1    ••  41  9        ]92 

TABLE  40.-SUMMER  LOW  AREAS. 


10000 

+13  1         04+88+41 

+46  1     +11  2        18  2          21  9 

9000 

-(-80    +16    +83     +  -5  3 

8000 

+  68    +03     +11  2    +42 

7000     . 

+28         38    +82     +61 

6000  . 

+  14  0          78         92        17  5 

6000    

+20  4          57        26  3        23  8 

>f48  4     -)-20  0    —38.1      40  4 

4000    

+18  5     +23  9       32  3        11  0 

3000  

+  65    +33  9        53  8     +  2  8 

+45  1     +55        19  2      16  6 

2000  

+38  6          23        50  2        19  2 

1000 

|365        13°        60  9     -   °9  9 

000 

+  15,7        15  4    69  1        31  4 

is  larger  than  MO  and  n  —  nc  is  positive,  it  follows  that  the 
temperature  gradient  is  smaller  for  n  than  for  n0,  and  if  n  is 
smaller  than  n0  the  temperature  gradient  is  larger  in  the  dis- 
turbed region  than  in  the  normal  undisturbed  stratum.  An 
examination  of  the  tables  and  the  fig.  14  shows  that  while  the 
distribution  of  n  —  na  is  similar  to  that  of  T —  T0  as  to  the  sec- 
tors, yet  there  is  a  distinct  reversal  between  the  lower  and  the  higher 
strata,  occurring  near  the  4000-meter  level.  The  positive  (+•) 
values  of  n  —  n0  in  the  lower  strata,  showing  a  decrease  of 
gradient  of  temperature  or  an  inflow  of  heat  on  the  western 
side  of  the  high  areas,  become  negative  (— )  values  in  the 
upper  strata,  where  they  indicate  a  more  rapid  loss  of  the 
temperature.  The  reverse  conditions  hold  on  the  -western 
half  of  the  low  areas  from  the  surface  to  10,000  meters. 
Hence  an  inflow  of  warm  air  in  the  lower  strata,  that  is  the 
southerly  current,  diminishes  the  normal  gradient  of  tempera- 
ture and  produces  n  —  «0  which  is  a  (  + )  quantity ;  similarly,  an 
inflow  of  cold  air  in  the  higher  strata,  that  is  of  cold  air  from 
the  north,  diminishes  the  normal  temperature  gradient  and 
produces  a  value  of  n  —  »?0  which  is  also  positive.  These  condi- 
tions are  therefore  in  harmony  with  the  observed  temperature 
distribution  in  cyclones  and  anticyclones.  The  reversal  be- 
tween the  lower  and  higher  strata  of  the  same  sectors  indi- 
cates the  thermodynamic  effect  of  the  air  masses  striving  to 
return  to  an  equilibrium  by  reversing  the  gradients  above 
and  below  the  level  of  4000  meters. 

VALUES  OF  THE  TERMS  —  Cf  H  (T —  TO)  AND  (z  —  ZQ). 

Having  determined  the  distribution  of  (  T —  T0)  and  (n  — »„) 
in  the  several  strata,  since  all  the  terms  of  the  equation,  except 
the  velocity,  depend  upon  them,  we  proceed  to  compute  these 
terms  for  the  sake  of  ultimately  finding  the  heat  variations 
Q  —  Q0 ,  and  the  barometric  pressure  variations  B  —  Z?0 .  The 
first  condition  to  be  found  is  g  (z  —  z0)  =  —  Cf  na  (  T —  T0 ) 
which  represents  the  available  potential  energy  of  the  air  mass 
at  a  given  level,  to  be  expended  in  producing  the  kinetic 
energy  found  in  cyclonic  and  anticyclonic  circulations.  Tables 
29,  30,  31,  32,  and  fig.  15  contain  the  several  terms.  — Cp  n0 
( T —  T0 )  is  the  potential  energy,  due  to  the  fact  that  the 
mass  of  temperature  T  on  the  level  where  T0  is  the  normal 
temperature  can  be  reduced  to  equilibrium  by  rising  or  fall- 
ing through  a  given  height  under  the  gravity  acceleration  g, 
where  g  (z  —  zc)  is  the  work  to  be  expended  in  falling  or  rising 
through  the  height  (2  —  z0).  The  value  of  g  is  given  on  each 
1000-meter  level.  The  height  (z  —  z0)  is  computed  from  the 
formula,  and  by  fig.  15  one  can  see  that  it  has  the  same  distri- 
bution as  (T — Tn),  upon  which  it  depends.  Thus,  the  posi- 
tive (  +  )  sign  for  (z  —  zo)  indicates  that  the  air  mass  is  too  cold 
for  its  level  and  that  it  can  fall  through  a  given  height  before 
reaching  the  normal  temperature  of  its  stratum;  similarly,  the 
negative  (— )  sign  for  (z — z0)  shows  that  the  air  mass  is  too 
warm  for  its  level  and  can  rise  through  a  given  height  to  reach 
equilibrium.  The  cold  sectors  have  the  (  +  )  sign,  and  the 
warm  sectors  the  ( — )  sign,  and  hence  the  entire  cold  column 
is  able  to  fall  and  the  entire  warm  column  can  rise  through 
(z  —  z0)  meters  under  the  influence  of  gravity.  This  is  the 
primary  source  of  the  energy  of  motion  in  cyclones  and  anti- 
cyclones, this  potential  energy  being  converted  into  pressure 
differences  and  motions. 

An  inspection  of  the  tables  and  the  fig.  15  shows  that  the 
maximum  potential  energy  is  on  the  east  and  west  sectors,  at 
the  boundary  of  the  high  and  low  pressure  areas.  Hence, 
there  is  a  gradient  of  potential  within  the  cold  areas  from  the 
north  toward  the  southeast  or  south,  and  within  the  warm 
areas  from  the  south  toward  the  northeast  and  north  at  all  the 
levels  except  that  next  the  surface.  The  difference  between 
the  lowest  level  and  those  above  it  must  represent  a  reaction 
from  the  ground,  and  an  accumulation  of  the  dynamic  effects 
from  the  other  forces  yet  to  be  considered,  such  as  those  from 


JUNE,  1906. 


MONTHLY  WEATHER  REVIEW. 


271 


the  horizontal  components,  the  deflecting  force,  the  friction, 
and  the  other  dynamic  effects.  Primarily,  we  must  recognize 
that  we  deal  here  with  a  couple,  one  branch  from  the  north  on 
the  west  of  the  cyclone,  and  the  other  from  the  south  on  the 
east  of  the  cyclone.  The  complex  interactions  which  occur  in 
consequence  of  these  dispositions  of  warm  and  cold  air  masses 
form  an  important  and  difficult  subject  of  study  in  hydrody- 
namics, which  must  be  considered  in  a  later  paper. 

DISTRIBUTION  OF  THE  VELOCITIES  <?,  J0,  £  (<?*  —  qj). 

Referring  to  the  figs.  6  and  7,  MONTHLY  WEATHER  REVIEW, 
March,  1902,  for  the  vectors  in  cyclones  and  anticyclones, 
which  were  derived  from  the  cloud  observations  made  by  the 
Weather  Bureau  in  1896-1897,  I  have  transferred  the  values 
for  the  several  gradients  to  Tables  33,  34,  35,  and  36  in  the  first 
section  q;  the  mean  value  of  the  (^-velocity  in  meters  per 
second  in  the  eight  sectors  of  the  corresponding  high  and 
low  areas  gives  the  mean  value  <?„;  from  these  are  computed 
i  (<?J  —  la)  which  are  plotted  on  fig.  16.  The  distribution  shows 
that  there  is  a  prevailing  northwest  cold  current  between  the 
high  and  low  areas,  and  a  southeast  warm  current  between 
the  low  and  high  areas.  The  maximum  values  of  |  (q'—q') 
occur  in  the  strata  that  are  elevated  6000-8000  meters  above 
the  surface,  and  the  values  are  somewhat  greater  in  the  cold 
than  in  the  warm  areas.  Attention  is  called  to  the  small  num- 
ber of  units  of  force  which  are  actually  expended  in  changing 
the  prevailing  velocities  of  the  eastward  drift,  in  comparison 
with  the  energy  available  in  the  potential  of  the  preceding 
terms. 

THE    DISTRIBUTION    OF    THE    HEAT,    Q  —  ()„. 

The  heat  term  is  computed  from  the  formula, 

Q-Q0=\  (i'+q')+CpT0  log  TO  (n-«0), 

using  the  values  given  in  the  preceding  tables,  first  in  mechani- 
cal units,  which  are  then  converted  into  calories  by  the  divisor 
4185.57.  The  results  are  tabulated  in  Tables  37,  38,  39,  and  40, 
and  the  distribution  is  shown  in  fig.  17,  which  is  quite  similar 
to  that  for  (n—na)  of  fig.  14,  since  the  term  Q  —  Qa  depends 
chiefly  upon  (n  —  nc).  There  is,  therefore,  the  same  reversal 
noted  as  in  the  previous  case,  the  positive  sign  (  +  )  denoting  a 
potential  energy  to  be  turned  into  heat  and  the  negative  sign 
(  —  )  an  amount  of  energy  to  lose  by  cooling.  One  can  not  but 
be  impressed  with  the  very  large  amount  of  heat  energy  here 
available,  in  comparison  with  which  the  kinetic  energy  of  mo- 
tion is  insignificant. 

This  may  be  the  proper  place  to  speak  of  the  efficiency  of 
the  atmosphere  as  a  thermal  engine.  By  analogy,  the  warm 
masses  are  in  the  boiler  and  the  cold  masses  are  in  the  con- 
denser. The  percentage  of  heat  actually  turned  into  kinetic 
energy  seems  to  be  very  small  and  the  efficiency  is  not  large. 
This  probably  comes  from  the  general  circumstance  that  air 
masses  can  lose  their  thermal  contents  only  by  action  on  their 
edges  or  surfaces,  the  interior  of  each  mass  holding  its  indi- 
viduality for  a  long  time  under  the  forces  which  tend  to 
destroy  it  by  working  slowly,  into  its  interior.  The  efficiency 
of  the  warm  and  cold  masses  under  atmospheric  conditions  is 
evidently  a  subject  which  will  demand  very  careful  considera- 
tion before  it  can  be  fully  analyzed  and  expressed  as  a  mathe- 
matical function. 

DISTRIBUTION  OF    THE  PRESSURES,   B  -  B^. 

We  approach  this  term  through  the  formula 


and  the  mean  density  I\  of  the  undisturbed  stratum,  except 
by  assuming  the  normal  conditions  there  found,  and  supposing 
that  the  local  variations  in  pressure  should  be  measured  from 
them.  It  was  for  this  purpose  that  these  tables  were  com- 
puted, in  order  that  they  might  ultimately  be  used  in  studying 

the  local  cyclonic  and  anticyclonic  variations. 


p 

As    °  can 


be 


The  term  —  °  is  computed  from  the  data  of  Tables  17  and  18, 

fa 

because  we  have  no  way  to  determine  the  mean  pressure  P0 


readily  computed,  its  values  will  not  be  introduced  into  this 
paper.  Furthermore,  it  is  necessary  to  compute  the  local  den- 
sity, />,  by  the  formula 

log  p  =  log/-,,  +  ^  (log  T-  log  T0) 

the  n  being  taken  as  the  mean  n  of  Table  16.  These  values 
are  also  omitted  because  of  the  magnitude  of  the  tables  that 
would  be  required  to  reproduce  them  in  this  place.  We 
finally  obtain  the  values  P  —  P0,  the  variation  of  the  pressure 
in  mechanical  units,  which  may  be  converted  into  millimeters 
by  the  formula, 

_     P        3 

=  100  X  4' 

The  resulting  values,  B  —  B0,  are  given  in  the  second  section 
of  Tables  37,  38,  39,  and  40  and  they  are  plotted  on  fig.  18. 
The  distribution  is  again  such  as  has  been  made  familiar  in 
the  preceding  figures  of  these  papers. 

These  pressure  differences  are  given  in  millimeters,  and 
they  represent  a  potential  energy  which  can  be  converted  into 
cyclonic  and  anticyclonic  motions  and  pressures.  The  fact 
that  the  observed  pressures  are  not  so  great  as  those  here 
given  shows  that  the  efficiency  of  the  kinetic  structure  is  not 
so  great  as  the  potential  energy  would  indicate.  Not  all  the 
available  energy  goes  into  storms,  a  portion  being  carried 
along  in  the  circulating  structures  without  transformation  and 
a  part  being  frittered  away  in  internal  work  agitations.  We 
have,  however,  shown  that  there  seems  to  be  an  abundant  sup- 
ply of  energy  in  warm  and  cold  masses  of  different  tempera- 
tures in  the  neighborhood  of  each  other,  sufficient  to  account 
for  all  the  phenomena  observed  by  meteorologists.  It  has 
been  proven  that  the  primary  distribution  is  asymmetrical  in  re- 
spect to  the  centers  of  the  low  and  high  pressure  areas.  It  is 
now  one  of  the  difficult  problems  to  show,  mathematically,  how 
the  action  of  these  cold  and  warm  masses,  arranged  as  couples 
between  the  dynamic  centers,  is  transformed  from  the  thermo  • 
dynamic  structures  here  indicated  into  the  hydrodynamic 
structures  actually  existing  in  the  atmosphere.  It  should  be 
remembered  that  the  closed  isobars  of  the  lower  strata,  prac- 
tically symmetrical  about  the  high  and  low  centers,  are  quickly 
modified  above  the  surface  into  loops  wherein  the  distribution 
of  the  pressure  is  entirely  different  from  that  at  the  surface 
as  shown  on  the  sea-level  weather  charts.  The  construction 
of  daily  and  monthly  isobars  on  the  3500-foot  plane  and  the 
10,000-foot  plane  for  the  United  States  during  the  year  1903 
made  this  change  of  the  structure  of  the  isobars  familiar  to 
me.  It  is  next  in  order  to  discuss  the  equations  in  the  hori- 
zontal plane,  namely, 

dq      dQ  dT  dn 

9rf-;=^-c^o^-c"r»lo^ro^ 

where  <r  is  a  line  in  the  plane  dx,  dy;  together  with  the  de- 
flecting forces  represented  by  the  terms, 

—  cos  0  (2 ta  -f  *)  vdx  +  cos d  (2 o>  +  v)  ud y, 

which  are  equal  to  zero,  so  far  as  the  circulation  is  concerned, 
since  vdx=  udy,  though  they  have  a  decided  effect  upon  the 
position  of  the  resulting  isobars;  and,  finally,  the  unknown 
terms  representing  the  secondary  or  vortical  motions  induced 
by  the  dynamic  motions  in  the  sensitive  hydrodynamic  medium 
of  the  atmosphere. 


XXXIV— 80, 


FIG.  14. — Distribution  of  the  values  of  n  —  n0  in  the  high  and  low  areas. 


_J-fa/?.       Jfegbf.        Jtfqh.          Low. 

/n  Steler^ . 


XXXIV— 81. 


FIG.  15. — Distribution  of  z  —  a.  = *_•  <T—T 

g      \  »- 


XXXIV— 82. 


FIG.  16. — Distribution  of  the  Telocity  term  \  (q*  —  5J0). 


XXXIV— 83. 


FIG.  17. — Distribution  of  the  heat,  Q  —  Q . 


XXXIV— S4. 


FIG.  18. — Distribution  of  the  pressure,  B  —  S0. 


DECEMBER,  1906 


MONTHLY  WEATHER  REVIEW. 


562 


in  the  cold  area,  G. 


.     ., 

in    UK      WitllU 


STUDIES  ON  THE  THERMODYNAMICS  OF  THE  ATMOS- 

PHERE. 
By  Prof.  FRANK  H.  BIGELOW. 

V.—  THE  HOKIZONTAL  CONVECTION   IN  CYCLONES  AND  ANTI- 

CYCLONES.1 

SOME  OF    THE  DIFFICULTIES  IN  THIS  PROBLEM. 

If  one  wishes  to  follow  the  exact  process  occurring  in  the 
natural  circulation  of  the  atmosphere,  then  the  next  step  in 
the  orderly  development  of  the  analysis  of  the  problem  of  the 
structure  of  cyclones  and  anticyclones  is  exceedingly  difficult, 
and  some  time  must  elapse  before  meteorologists  will  be  able 
to  complete  the  solution  in  a  rigorous  manner.  This  may  be 
explained  by  resuming  our  study  of  the  interchange  of  energy 
in  the  nonadiabatic  circulation  between  high  and  low  areas.2 
Equations  (44)  and  (52),  so  far  as  they  relate  to  the  circula- 
tion in  a  horizontal  plane  x  y,  in  the  integrated  form  give  the 
following  : 

cx(r-r0)  +  cp  TO  log  TO  (»-«„)  =  (O-OJ-i  (?2-90s). 

Since  there  is  to  be  an  interchange  of  energy  between  the 
cold  area,  whose  center  will  be  marked  C,  and  the  warm  area 
whose  center  is  W,  the  following  notation  will  be  employed: 

n0  ,  the  gradient  ratio3 

T0  ,  the  temperature 

<?0  ,   the  vector  velocity 

Q0  ,  the  heat  energy 

n  ,    the  gradient  ratio3  1 

T,  the  temperature      I 

,-i  j  i        •  L       r 

q  ,    the  vector  velocity 
Q  ,  the  heat  energy      \ 

The  C  and  W  areas  lie  between  the  centers  of  high  and  low 
pressure,  marked  H  and  L,  respectively,  in  the  order  from 
west  to  east,  as  follows: 

if  (high);   (7  (cold);  L  (low);   W  (warm); 

as  illustrated  in  the  diagrams  of  papers  No.  I,  II,  III,  and  IV 
of  this  series.  (MONTHLY  WEATHER  REVIEW,  1906,  January,  Feb- 
ruary, March,  and  June,  respectively.) 

(A)  One  problem  is  to  show  the  relations  between  the  ther- 
modynamic  centers  G  and  W,  and  the  hydrodynamic  centers 
H  and  L  in  the  moving  atmosphere.     It  will  not  be  proper  to 
make  model  circulations  by  erecting  chambers  around  given 
masses,  and  then  removing  certain  internal  partitions.     This 
process  really  evades  the  entire  problem  to  be  solved,  and 
substitutes  some  ideal  or  experimental  system  in  place  of  that 
occurring  in  the  atmosphere. 

(B)  Another  problem  is  concerned  with  the  gradient  factors 
()i0  and  n)  and  the  temperatures  (T0and  T),  and  may  be  stated 
in  the  following  form.     Since   the  gradients  of  temperature 
are  changing  from  point  to  point  in  the  vertical  and  in  the 
horizontal  directions  in  a  very  complex  fashion,  it  seems  im- 
practicable to  assign  temperature  functions  in  advance  of  the 
actual  observations,  and  therefore  analytic  formulas  of  suffi- 
cient flexibility  to  express  the  entire  existing  conditions  are 
impossible.    If  a  simple  function  of  the  temperature  is  adopted, 
it  is  certain  that  this  functon  will  not  be  applicable  to  the  cy- 
clonic structure  taken  as  a  whole,  and  hence  it  is  very  hard  to 
derive  the  pressures  from  the  temperatures  by  the  simple 
quasi-adiabatic  formulas. 

(C)  Furthermore,  the  most  troublesome  problem  of  all,  in 
the  present  state  of  meteorology,  is  to  show  what  is  the  rela- 
tion between  the  velocity  terms  (q0  and  q)  and  the  heat  terms 
(<50  and  Q).     The  cyclonic  circulation  constitutes  an  effort  to 
bring  back  to  equilibrium  the  energy-difference  represented 
in  the  cold  and  warm  areas,  and  this  is  done  by  setting  up  an 

'This  paper  logically  follows  No.  IV,  in  the  Review  for  June,  1906,  but 
its  publication  has  been  delayed.  —  EDITOB. 

2  See  Monthly  Weather  Review,  March,  1906,  page  114. 

3  See  Monthly  Weather  Review,  March,  1906,  page  113. 


extensive  series  of  internal  vortices,  graduated  in  size  from  the 
large  storm  areas,  down  thru  tornadoes  or  secondaries  to 
the  minute  whirls  that  are  not  accessible  to  any  instrumental 
records.  In  this  interchange  of  heat  between  the  warm  and 
cold  masses,  a  portion  of  the  energy  is  absorbed  in  maintain- 
ing the  velocity  of  the  masses  of  air,  a  second  portion  goes 
into  radiation,  and  a  third  part  into  equalizing  the  tempera- 
tures. The  velocity  of  the  wind  in  a  cyclone  does  not  measure 
the  true  velocities  (q0  and  q),  since  the  latter  include  the  total 
internal  circulation  as  well  as  the  flow  of  the  main  stream; 
but  there  seems  to  be  no  way  to  separate  these  parts  from  one 
another.  In  a  word  the  total  energy  is  given  by  the  terms 

Gpn0  (T-  T0)  +  Cp  T,  log  T9  (n-nj, 

but  I  can  as  yet  discover  no  method  of  distributing  the  re- 
spective portions  of  this  total  among  the  equivalent  terms, 
(0-0.)  -  i  (q'-qj)  +  radiation. 

Until  all  these  difficulties  have  been  overcome  it  will  be 
possible  to  make  only  tentative  and  incomplete  discussions  of 
the  great  problem  involved  in  analytic  meteorology. 

(D)  Finally,  the  general  question  as  to  the  reason  why  the 
observed  gradients  of  temperature  differ  from  the  adiabatic 
gradient  is  closely  bound  up  with  the  distribution  of  the 
available  energy  between  the  q  and  Q  terms.  If  a  mass  of  air 
is  moved  from  one  level  to  another,  as  from  5000  meters  to 
4000  meters,  in  an  adiabatic  atmosphere,  the  pressure  and  the 
temperature  change  according  to  the  adiabatic  law;  in  a  non- 
adiabatic atmosphere,  the  change  of  temperature  does  not 
correspond  with  the  pressure,  but  a  divergence  exists  depend- 
ing on  the  proportion  represented  by  the  difference  of  the 
ratios  n  —  n0.  If  in  a  nonadiabatic  atmosphere  there  is  ver- 
tical displacement  of  an  air  mass,  the  interchange  of  energy  is 
partly  as  heat  and  partly  as  velocity,  and  at  the  moment  a  mass 
moving  adiabatically  in  the  midst  of  a  nonadiabatic  mass 
arrives  at  such  a  displacement,  z  —  z0,  as  to  be  appreciable  in 
respect  to  n  —  n0,  there  is  set  up  a  small  local  interchange  of 
energy  between  these  masses  in  the  form  of  a  minor  gyration 
of  some  sort.  There  is  thus  a  continual  tendency  to  balance 
these  two  expenditures  of  energy,  the  one  against  the  other, 
in  the  most  economical  way,  and  the  resultant  temperature  and 
circulation  represents  the  outcome  of  this  physical  process. 
(See  fig.  19.) 

If  instead  of  one  rising  current  of  warm  air,  A  0,  which  be- 
comes overcooled,  and  one  current  of  cold  air,  E  W,  which  be- 
comes overheated  by  adiabatic  expansion  and  contraction  with 
the  change  of  level,  there  are  several  such  rising  and  falling 
masses  in  a  series  stretching  from  west  to  east,  the  interchange 
of  heat  becomes  more  complicated.  Thus  the  cold  mass  G  will 
be  found  between  two  masses  of  warm  air  W,  and  the  warm  mass 
between  two  cold  masses  on  the  same  horizontal  level.  In 
this  case  each  warm  mass  W  will  divide  and  seek  G  G  on  either 
side  of  it;  the  cold  mass  will  also  divide  and  seek  W  W  on 
either  side.  Since  these  small  horizontal  currents  can  not 
flow  together  from  opposite  directions  to  the  center  because 
a  congestion  of  mass  would  occur,  the  motion  is  transformed 
into  an  inflowing  helix  with  vertical  component  upward  for  a 
low  pressure  center  L,  and  a  counterflowing  helix  with  down- 
ward vertical  component  with  a  high  pressure  H  at  the  center 
of  the  vortex.  This  process  is  the  cause  of  the  minor  whirls  in 
the  atmosphere,  and  contributes  something  to  the  formation 
of  cyclones  and  anticyclones.  In  the  latter  case  the  warm 
and  cold  masses  are  not  produced  by  vertical  adiabatic  changes, 
but  by  transportation  of  horizontal  currents  from  great  dis- 
tances. The  same  tendency  to  divide  the  warm  mass  in  the 
northern  quadrants  between  the  low  and  high  pressure  centers 
and  to  curl  the  cold  mass  into  two  branches  in  the  southern 
quadrants  of  the  high  and  low  pressure  areas,  has  been 
already  found  in  the  observations  of  the  stream  lines  and  the 
distribution  of  the  temperatures.  The  tendency  to  divide  and 


563 


MONTHLY  WEATHEK  EEVIEW. 


DECEMBER,  1906 


curl  about  the  respective  branches  is  common  to  all  mixing 
masses  of  different  temperatures. 

'Zenith 


/kfual  counter  floits  \     Radial  counter  f/otos 
J? 


C~-  Cotcl 


JV- 


FIG.  19.— Scheme  of  the  transformation  of  adiabatic  gradients  into  ob- 
served temperature  gradients  thru  the  heat  terms  ( Q  —  §„)  and  velocity 

terms    (g' — g 


A  E=  Observed  nonadiabatic  gradient. 
A  C=  Adiabatic  gradient  for  warm  rising  air. 
E  W=  Adiabatic  gradient  for  cold  descending  air. 
CD  =  Quantity  of  heat  -f  Ql  to  be  added  to  restore  the  equilibrium  at 

the  height  z  —  z0. 
WD  =  Quantity  of  heat  —  Q0  to  be  lost  in  restoring  the  equilibrium. 

At  the  level  C  D  TV  other  amounts  of  heat,  +  A  Qv  —  A  Q0,  are  expended 
in  setting  up  a  velocity  g0  which  is  converted  into  a  vortex  with  a  vertical 
component. 

If  we  find  an  adiabatic  rate  of  temperature  fall  in  the  Tropics 
such  as  10.0°  C.  per  1000  meters,  but  one  of  5.0°  C.  in  the 
temperate  zones,  and  of  only  2.0°  C.  in  the  polar  zones,  then 
this  distribution  between  the  Tropics  and  the  polar  zones  is 
maintained  by  circulation  and  heat  interchange.  The  streams 
of  warm  air  in  the  lower  strata,  0  to  3000  meters,  and  in  the 
upper  strata,  10,000  to  14,000  meters,  on  moving  from  the 
Tropics  to  cooler  latitudes,  gradually  lose  heat  by  expending 
the  energy  thru  a  series  of  minor  and  major  gyrations  which 
are  set  up.  These  streams  near  the  surface  tend  by  their 
rising  to  higher  levels,  as  they  approach  the  polar  zones,  to 
stratify  the  warmer  air  higher  up  in  proportion  to  their  de- 
parture from  the  Tropics,  and  thus  to  lessen  the  temperature 
fall  from  the  surface;  likewise,  above  the  10,000-meter  level 
the  same  phenomenon  occurs.  Similarly,  the  cold  polar  cur- 
rents flowing  toward  the  equator  tend  to  sink  to  lower  levels, 
and  this  diminishes  the  temperature  gradient  in  the  middle 
latitudes.  These  two  systems  of  currents  can  not  traverse  the 
space  between  the  Tropics  and  the  polar  zones  without  en- 
countering one  another,  and  interacting  upon  each  other,  in 
the  cyclones  and  anticyclones,  and  the  general  effect  of  the 
entire  process  is  to  maintain  a  gradient  of  temperature  which 
differs  from  the  adiabatic  rate.  The  divergence  between  the 
actual  and  the  adiabatic  rate  is  very  different  from  place 
to  place,  as  shown  by  the  observations.  There  is  an  incessant 
turmoil  of  adjustment  at  all  levels,  and  in  all  latitudes,  whose 
outcome  is  the  wind,  clouds,  rain,  and  temperature  actually 
prevailing.  As  above  stated,  it  seems  to  be  impossible  to  treat 
this  physical  complex  as  an  analytic  unit  in  the  present  state 
of  meteorology,  and  hence  I  shall  confine  my  discussion  to  a 
series  of  more  or  less  detached  studies,  which  yet  tend  to 
elucidate  the  general  problem. 


THE    HORIZONTAL    CIRCULATION. 

In  Tables  29  and  30,*  under  the  columns  z — z0,  are  given  the 
vertical  distances  thru  which  the  cold  masses  must  fall  and  the 
warm  masses  rise,  in  order  to  attain  an  equilibrium  on  their 
respective  levels.  Thus,  for  the  maximum  cold  masses  in  the 
east  quadrant  of  the  high  area  and  the  west  quadrant  of  the 
low  area,  and  for  the  maximum  warm  masses  in  the  west  quad- 
rant of  the  high  area  and  the  east  quadrant  of  the  low  area,  we 
find  the  displacements  in  the  winter,  respectively,  as  follows: 

TABLE  41. —  Vertical  displacement,  z  —  zc,  from  equilibrium. 


Height  in 
meters. 

HiKli 
east. 

Low 
west. 

Mean. 

High 
west. 

Low 

east. 

Mean. 

10000  

+325 

+  454 

+890 

—  325 

—487 

-406 

9000  

+366 

+440 

+403 

-  352 

—440 

-39li 

8000  

+  425 

+467 

+446 

—  425 

-382 

-404 

7000  

+498 

+498 

+498 

-  569 

—356 

—463 

6000  

+592 

+563 

+678 

-  740 

—326 

—533 

5000  

+748 

+650 

+699 

-  926 

-325 

—626 

4000  

+793 

+646 

+720 

-1033 

-333 

—633 

3000  

+854 

+726 

+790 

-1024 

—299 

-662 

2000  

+984 

+777 

+  881 

—1036 

—311 

—674 

1000  

+836 

+  593 

+715 

—  890 

—351 

-621 

0  

+511 

+414 

+  463 

—  487 

—268 

—378 

The  sign  (  +  )  means  that  the  mass  is  too  high  by  the  given 
number  of  meters  for  thermodynamic  equilibrium,  and  the  sign 
( — )  that  the  mass  is  too  low.  The  cold  masses  can  fall  thru 
2— zc  meters  and  the  warm  masses  can  rise 
on  their  respective  levels,  under  the  given  conditions. 

C 


thru  2 — 20  meters 


Cold 


FIG.  20. — The  conversion  of  vertical  falls  into  hoiizoutal  circulation. 

Thus  at  the  4000-meter  level  the  cold  mass  can  fall  about 
720  meters  and  the  warm  mass  can  rise  683  meters  to  bring, 
about  thermal  equilibrium,  when  there  is  no  horizontal  circulation. 
If  the  cold  air  could  sink  to  the  level  of  the  warm  mass  ther- 
mally, it  would  have  a  potential  fall  of  1403  meters,  supposing 
this  warm  mass  to  remain  unchanged  in  position  and  energy. 
The  tendency  is  then  for  the  cold  mass  in  seeking  the  lowest 
thermal  level  not  to  fall  vertically,  but  in  the  main  to  move  almost 
horizontally  down  a  gradient  defined  by  G  W.  Assuming  that 
the  distance  between  the  maxima  C  and  W  averages  as  in  the 
ordinary  cyclone  about  1000  kilometers,  or  1,000,000  meters 
we  have  a  possible  gradient, 

G  ==  tan  -'  L  QQO  OQU  j  =  tan  -  '  (0.001403)  =  0°  5'  3". 

As  this  large  gradient  would  give  very  rapid  horizontal  mo- 
tions there  is  too  much  power  to  be  expended  in  this  simple 
manner.  The  warm  mass  is  really  rising  and  the  cold  mass 
falling  simultaneously,  not  vertically  but  toward  each  other 
in  the  manner  indicated  by  the  diagrams,  figs.  9, 10. 6  In  these, 
and  from  other  descriptions  of  the  prevailing  circulation  found 
in  the  reports  of  the  Weather  Bureau,  we  infer  that  in  all  of 
the  levels  the  cold  current  flows  southeastward  toward  the 
warm  area,  while  the  warm  current  flows  northwestward  toward 
the  cold  area. 

This  flow  is  not  directly  toward  the  respective  centers  of  the 
warm  and  cold  waves,  making  the  currents  meet  along  an  axis, 

4  See  Monthly  Weather  Review  for  June,  1906,  pp.  267-271. 
6  See  Monthly  Weather  Review,  February,  1906,  pp.  77-78  and  litho- 
graph plate  at  the  end. 


DECEMBER,  1906. 


MONTHLY  WEATHER  REVIEW. 


564 


because  this  would  produce  a  congestion  of  the  density  and 
make  the  flow  impossible.  The  system  of  internal  reactions 
in  the  circulating  fluid,  in  combination  with  the  deflecting 
force  due  to  the  earth's  rotation,  will  cause  the  stream  lines 
to  flow  about  the  center  up  to  a  certain  limited  amount  of  con- 
gestion on  the  outer  circles.  It  is  evident  that  a  compromise 
or  resultant  between  these  opposite  tendencies  must  be  brought 
about,  and  then  the  stream  lines  will  approximate  to  spirals  con- 
verging toward  the  center  in  the  cyclone,  but  diverging  in  the 
anticyclone.  In  order  to  avoid  the  congestion,  a  vortex  motion 
is  thus  established  with  an  ascending  component  over  all  areas 
contained  within  the  closed  isobars  of  the  cyclone,  but  descend- 
ing in  the  anticyclone.  The  conflict  of  this  localized  circulation 
with  the  general  circulation,  the  continuous  absorption  of  the 
former  by  the  latter,  produces  the  entire  observed  cyclone  sys- 
tem. Quite  similar  reasoning  accounts  for  the  downward  com- 
ponent in  the  anticyclone,  which  is  generated  and  fed  from  the 
other  portions  of  the  cold  and  warm  areas,  since  it  has  been 
shown  that  both  of  these  masses  divide  into  two  branches  and 
are  absorbed  in  consecutive  high  and  low  pressure  areas. 


FIG.  21 Scheme  of  the  horizontal  circulation  in  cyclones  and  anti- 
cyclones. 

In  the  low  area,  in  the  strata  from  the  surface  to  about  4000 
meters,  to  the  southward  of  the  center,  the  cold  mass  tends  to 
underrun  the  warm  mass,  while  to  the  northward  of  the  cen- 
ter in  the  strata  above  4000  meters,  the  warm  mass  tends  to 
overflow  the  cold  mass.  On  the  other  hand,  in  the  high  pres- 
sure area,  similar  conditions  exist  tho  the  sectors  or  quadrants 
are  inverted  in  their  order.  The  cold  air  near  the  surface 
separates  or  divides  into  two  branches,  which  tend  to  under- 
run  the  warm  areas  on  either  side,  and  in  the  high  levels  the 
warm  air  divides  into  two  branches  which  tend  to  overflow  the 
adjacent  cold  masses  on  either  side. 

Cold  Warm  Cold 

•-i 


In  the  warm  areas  the  isobars  are  farther  apart  than  in  the 
cold  areas,  and  by  the  ordinary  rules  the  circulations  are  in 
the  directions  indicated.  The  warm  mass  divides  into  two 
branches  which  overflow  the  cold  masses  to  the  north,  while 
the  cold  mass  divides  into  two  branches  which  underrun  the 
warm  masses  to  the  south.  The  outcome  is  to  produce  more 
stable  equilibrium  by  superposing  air  of  less  potential  density 
upon  air  of  greater  potential  density.  At  the  same  time  there 
is  an  interchange  of  heat  and  a  manifestation  of  dynamic 
energy  in  the  form  of  large  and  small  vortices  on  the  hori- 
zontal planes  with  dynamic  components  in  the  vertical  direc- 
tions. In  this  process  there  are  involved:  (1)  an  interchange 
of  heat;  (2)  a  more  stable  equilibrium,  since  gravity  has  pulled 
the  air  of  great  potential  density  downward,  while  that  of 
lower  potential  density  is  pushed  up;  (3)  an  amount  of  kinetic 
energy  corresponding  to  the  movements  of  the  air  masses  from 
one  level  surface  to  another;  (4)  important  horizontal  motions 
with  minor  vortex  motions  whose  kinetic  energy  represents  a 
large  fraction  of  that  mentioned  in  the  preceding  item. 

THE  HORIZONTAL  PRESSURE  GRADIENTS. 

In  order  that  the  reason  for  this  overflow  of  warm  masses 
upon  cold  masses  in  the  upper  strata,  with  underflow  of  cold 
masses  beneath  warm  masses  in  the  lower  strata  may  be  evi- 
dent, we  need  only  compute  the  pressures  B  in  the  several 
strata  of  the  warm  and  cold  masses,  respectively,  from  the 
surface  up  to  10,000  meters.  Combine  the  temperatures  given 
in  Table  216  thus:  Take  the  mean  of  the  temperatures  of  the  east 
sector  of  the  high  area  and  the  west  sector  of  the  low  area  for 
the  mean  temperature  in  the  cold  mass,  and  the  mean  of  the 
temperatures  of  the  west  sector  of  the  high  area  and  the  east 
sector  of  the  low  area  for  the  mean  temperature  of  the  warm 
mass,  on  each  of  the  1000-meter  levels.  The  result  will  be 
found  in  Table  43,  Section  II,  and  is  transferred  to  the  first 
column  of  the  cold  and  warm  masses  in  Table  42,  and  marked  t. 

The  mean  t  of  the  successive  strata  gives  the  mean  tempera- 


! ,  in  the  second  column.    This 


Cold  Warm  Cold  Warm/  Cold 

FIG.  22. — Illustrating  the  relation  of  the  thermodynamic  gradients  to 
the  hydrodynamic  pressures  in  cyclones  and  anticyclones. 


ture  of  the  air  column,  0=         * 

2 

is  the  argument  for  m  in  Table  91,  International?  Cloud  Report, 
and  we  may  assume  that  the  observed  t  is  the  virtual  tempera- 
ture, and  that  it  includes  the  dry  air  and  the  vapor  contents  as 
they  occur.  With  H  the  height  and  &  as  arguments,  the  value  of 
m  is  extracted.  It  is  now  necessary  to  assume  some  value  of  the 
pressure  B  at  the  surface  in  warm  and  cold  areas,  independent 
of  any  variation  due  to  the  circulation  in  the  high  and  low 
areas,  and  I  have  taken  two  pressures,  10  millimeters  different, 
as  fairly  representing  known  surface  pressures  under  the  pre- 
scribed conditions.  Thus,  for  770  millimeters  in  the  cold 
mass,  we  shall  have  760  millimeters  in  the  warm  mass,  as  the 
barometric  pressure  at  the  surface.  Adopt  these  values,  take 
log  B,  2.88649  in  the  cold  area,  2.88081  in  the  warm  area,  add 
successively  the  m  on  the  several  levels,  and  then  take  the 
corresponding  Bc,  Bw.  Comparing  Bc  with  Bw  it  is  seen  that 
the  cold  area  pressure  is  greater  than  the  warm  area  pressure 
up  to  4000  meters,  and  that  the  warm  area  pressure  is  greater 
than  the  cold  area  pressure  above  that  level.  Hence,  cold  air 
flows  to  warm  areas  below,  while  warm  air  flows  to  cold  areas 
above  4000  meters,  conforming  to  well-recognized  principles. 
We  can  compute  the  vertical  distance  thru  which  1  milli- 
meter of  air  extends  in  the  several  levels.  Take  the  difference 
between  the  pressures  in  the  successive  1000-meter  levels, 
B  —  50,  the  second  difference,  J  (B  —  50),  showing  the  varia- 
tion with  the  height,  then  divide  1000  by  B  —  50  for  J  z,  the 
required  height  in  meters  thru  which  1  millimeter  of  air,  that 
is  the  weight  of  air  measured  by  1  millimeter  of  mercury, 
extends.  It  changes  from  11  meters  near  the  surface  to  31 
meters  near  the  10,000-meter  level,  and  shows  the  spaces  that 
exist  in  a  vertical  direction  between  successive  isobaric  surfaces. 

•  Page  268,  Monthly  Weather  Keview,  June,  1906. 


565 


MONTHLY  WEATHER  REVIEW. 


DECEMBER,  1906 


Since  the  tendency  of  gravity  is  to 
the  same  stratum,  a  circulation  is 
this  is  the  flowing  of  the  air  whic 
observed  cyclones  and  anticyclon 
other  forces,   inertia,   expansion  i 
centrifugal,  friction,  and  internal 
plex  network  of  forces  can  be  redi 
cussioii  only  with   the  greatest  c 
term  involving  the  interchange  o 
and  it  seems  nearly  useless  to  atte 
mental  knowledge  of  this  proces 
obtained  by  a  careful  discussion  of 
observed  in  balloon  and  kite  ascen 

TABLE  42.  —  Computation  of  the  pressure  1 
each  1000-mete 

make  these  spaces  equal  in                                                       TABLE  43. 
set  up  to  bring  this  about;           I.—  Mean  values  of  the  gradient  ratio  n  in  the  cold  and  warm  maxima. 

h,  thereupon,  builds  up  the 
38  in  combination  with  the       Hci,Mt 
ind  contraction,  deflection,     in  mricrx 
rortical  motion.     This  corn- 
iced to  a  rigid  analytic  dis- 
ifficulty    even  without  the     10000  

Ratio.        n 
High      Low    Mean 
east.     west.     cold. 

Ratio.         n, 
High      Low    Mean 
west.     east.    warm. 

W—  C 

Mean 

"0 

1.778    1.659    1.718 
1.637    1.500    1.618 
1.495     1.443     1.469 
1.523    1.447     1.485 
1.567    1.498    1.533 
1.  623     1  .562     1.  593 
1.726     1.690     1.708 
1.894    1.870    1.885 
2.285    2.160    2.218 
2.179    2.213    2.196 
1.769    2.065    1.917 

1.535     1.547     1.541 
1.319     1.458    1.389 
1.246     1.447     1.347 
1.234     1.471     1.353 
1.272    1.518    1.395 
1.430    1.629    1.530 
1.974    1.766    1.870 
2.443    1.974    2.209 
3.056    2.618    2.787 
3.439    2.611    3.026 
3.290    2.367    2.829 

—.177 
-.129 
—  .  122 
-.182 
138 

1.630 

1.454 
1.408 
1.  119 
1.464 
1.562 
1.789 
2.047 
2.503 
2.611 
2.373 

f  heat  energy  into  velocity,      9000  

nipt  it  until  further  experi-      gooo 

Sin  the  free  air  has  been 

,.,.                 7000... 

the  temperature  conditions 

6000 

sions. 

i  in  the  cold  and  warm  maxima  on 
r  level.                                                   4000 

—.063 
+.162 
+.324 
+.669 
+.829 
+  .912 

Height 
in 
meters. 

In  cold  masses. 
I            9           m           Bo           Be 

3000 

In  warm  masses. 
2000 

(               «         m             Bw          Bw 
1000  

10000... 
9000... 
8000... 
7000... 
6000  .. 
5000... 
4000.. 
3000... 
2000... 
1000... 
0... 

°C.       °C.                    log.        mm. 
—56.6                               2.28423    192.41 
—53.  6    6796 
—50.5                               2.35219    225.01 
—47.2    6561 
—43.8                              2.41780    261.70 
—40.  5    6371 
—37.1                                 2.48151     303.05 
—33.9    6195 
—30.6                               2.54346    349.61 
—27.5    6033 
—24.3                                 2.60379    401.60 
—21.3    5885 
—18.2                                 2.66264    459.86 
-15.5    5752 
—12.7                               2.72016    625.00 
-10.2    5636 
—  7.  6                               2.  77662    597.  75 
—  5.  5    5536 
—  3.  3                              2.  83188    679.  02 
—  0.  8    5461 
+  1.7                              2.88649    770.00 

°  C       °C.                      log.        mm.           000 

—51.7                                2.29445    196.99 

—45.  0                          2.  36040   229.  30            II.  —  Mean  values  of  the  temperature  T  in  the  cold  and  warm  maxima 

—41  4     6397 

—37.  8                                2.  42437    265.  69 
—34.1    6200 
—30.4                                2.48637    306.46          Hefeht 
-26.8    6016                                     in  meters. 
-23.1                                   2.54653    851.99 
-19.7    5849 
—16.2                                2.60502    402.74 

Temperature,      t 
High      Low    Mean 
east.     west.     cold. 

Temperature.      ^ 
High      Low    Mean 
west.     east.    warm. 

w-c. 

Mean 

<o+273° 

Log.  T0 

—13.4    5705 
-10.1!                                 2.66207    459.27 
—  8.  3    5595                                      10000  

®c       ^c      ^c 

—56.2    -57.0    —66.6 
—50.2    —50.7     -50.5 
—43.6    —43.9    —43.8 
—37.1    —37.1    —37.1 
—30.7    —30.5    —30.6 
—24.6    —24.0    -24.3 
—18.6    -17.8    -18.2 
—13.0    -12.4    —12.7 
—  8.0    —  7.2    —  7.6 
—  3.  7    -  2.  8    —  3.  3 
+  1.5     +  1.9    +  1.7 

—  52.'2    -51.'2    —  51.'7 
—45.3    —44.7    —45.0 
—87.6    -87.9    —37.8 
—29.6    -31.1    —80.4 
—21.7    —24.5    -23.1 
—14.3    —18.0    —16.2 
87        12  5        10  6 

+4.9 
+6.5 
+6.0 
+6.7 
+7.5 
+8.1 
+7.6 
+6.8 
+6.0 
+5.0 
+3.5 

Ab.i. 
218.8 

225.2 
232.2 
239.2 
246.1 
152.7 
258.6 
263.7 
268.4 
272.2 
276.5 

2.34005 
2.  35257 
2.36586 
2.  37876 
2.39111 
2.40261 
2.  41263 
2.42111 
2.42878 
2.  43489 
2.  44170 

—  5.  9                                2.  71802    622.  42 
—  3.7    5499                                           9000  
—  1.  6                                2.  77301    592.  94 
0.  0    5425                                        8000  

+  1.7                                2.82726    671.83 
+  3.5    5355                                        7000  
+  5.2                                2.88081    760.00 
6000  

Vertical  distance  for  1  mm.  of  pressure  beh 

eeen  strata  of  different  temperature.       5000 

Height. 

B-B,  A(JJ-J?0)   (S-Ba)      A,          A, 

4000 

B—Bty  A  \B  —  BQ)  \B—B())        At         A( 
3000  

—  4.  2    —  7.  6    —  5.  9 

10000... 
9000... 
8000... 
7000... 
6000... 
5000... 
4000... 
3000... 
2000... 
1000... 
0... 

mm.       mm.         log.         log.        mm. 

32.60                   1.61322    1.48678    30.68 
4.09 
36.69                    1.56455     1.43545    27.25 
4.66 
41.35                    1.61648    1.38352    24.18 
5.11 
46.46                  1.66708    1.33291    21.52 
5.63 
52.09                  1.71675    1.28325    19.20 
6.17 
58.26                  1.76537    1.23463    17.16 
7.08 
66.14                  1.81385    1.18615    15.35 
7  61 
72.75                  1.86183    1.13817    13.75 
8.52 
81.27                  1.90993    1.09007    12.30 
9.71 
90.98                  1.95895    1.04105    10.99 

-  0.  2    -  3.  0    —  1.  6 

+  2.7    +0.7    +1.7 
+  5.6    +4.7     +5.2 

32.31                    1.50934    1.49066    30.95        1000 

4.08 
36.39                      1.56098    1.43902    27.48           000 

4.38 

4.76                                                   III.—  Mean  values  of  the  velocity  term  m  the  cold  and  warm  maxima. 

5.22 
50.75                      1.70544    1.29456     19.70 
5.78                                                         Height 
56.53                    1.75228    1.24772    17.69       in  meters. 
6.62 
63.15                    1.80037    1.19963    15.84 
7.37 

Velocity.      K?!1-?2) 
High      Low    Mean 
west.      east.    warm. 

Velocity.      H?!2—  <P\ 
High      Low    Mean 
east.     west.     cold. 

Average. 

70.52                    1.84831    1.15169    14.18 
8  37                                                      10000 

+54      +175      +115 
+56      +216      +136 
+72      +228      +160 
+72      +220      +146 
+65      +160      +113 
+88      +88      +88 
+72      +72      +72 
+60      +86      +73 
+  10      +52      +31 
+  3       +19       +11 
+  8      +18      +13 

-127     —  95     —111 
—122      —122      —122 
—101      —132      -117 

113 
129 
134 
126 

98 
75 
58 
55 
30 
15 
11 

78.89                    1.89702    1.10298    12.68 
9.28                                                        9000  
88.17                    1.94532    1.05468    11.34 

THE    HORIZONTAL    INTERCHAN 

We  can  secure  some  idea  of  1 
interchange  of  the  heat  energy  01 
a  computation  of  the  formula: 
Term  I                  Term  II 

The  necessary  data  are  collected 
gathered  in  the  same  way  as  desc 

OE    OF    HEAT   ENERGY.                                gooo 

—  83      —  83      —  83 
—  74      —  50      —  62 
—  66      —  32      —  44 
-  68      —  14      —  36 
—  28      —  28      —  28 
—  12      —  25      -  19 
—    8      —    8      —    8 

he  process  involved  in  the 

i  the  horizontal  surfaces  by 

4000  
3000  

in  Table  43,  and  they  are      1000  
ribed  for  the  temperatures,       ooo  

by  combining  the  sectors  of  cold  and  of  warm  masses,  respect- 
ively. The  mean  value  of  the  gradient  ratio  n  is  found  by 
extracting  n  from  Tables  25  and  26,  and  taking  the  means, 
n  for  cold  areas  and  nl  for  warm  areas.  Then  the  difference, 
n,  —  n,  and  the  mean,  n0  =  \  (n  +  «,),  are  taken  out  for  use  in 
the  formula.  We  adopt  the  notation  (n,  t,  q,  Q)  for  the  cold 
mass,  (n  ,  <,,  qv  Qt)  for  the  warm  mass,  and  (nc,  <0,  qa,  Q0)  the 
mean  values  of.  the  cold  and  warm  masses  when  required. 


These  data  are  given  in  Section  I  of  Table  43;  the  tempera- 
ture data  in  Section  II  of  that  table  are  taken  from  Tables  21 
and  22;  T0  and  log  T0  are  computed;  finally,  |  (q*  —  g2)  are 
taken  from  Tables  33  and  34.  Since  the  velocity  energy  is  a 
small  term  in  comparison  with  (Qt  —  Q),  there  is  no  need  to 
be  particular  about  the  exact  velocities,  and  approximate 
values  are  sufficient.  In  order  to  learn  the  relation  between 
the  values  of  the  ratio  n,  n1  in  cold  and  warm  areas  in  the 


DECEMBER,  1906. 


MONTHLY  WEATHEE  REVIEW. 


566 


several  strata,  they  are  plotted  in  fig.  23.  It  is  seen  that  the 
curves  cross  each  other  between  the  4000  and  the  5000-meter 
level,  showing  that  there  is  a  reversal  of  the  physical  process 
at  that  elevation,  as  warming  below  and  cooling  above,  so  that 
the  cold  mass  is  warming  below  and  the  warm  mass  is  cooling 
above  in  conformity  with  the  preceding  statements.  Since 
the  adiabatic  gradient  is  —9.87°  C.  per  1000  meters,  and 

a  =  a°,  we  find  the   gradients  corresponding  with  n  at  the 

several  levels  by  using  the  lower  horizontal  argument  in  the 
diagram. 


/oooo 

9000 

8000 

JOOO 
60OO 

ffooo 

4OOO 
3OOO 
2000 

/ooo 

000 

***       ZK 

2 

w 

// 

/ 

\\ 

\ 

k 

V 

\^ 

v^ 

\, 

"*->-. 

^ 

^ 

^x 

N 

7 

& 

y 

a0-9.87 
n,     l.o                  /,5                  2.0                  25                 3.0 
0.   ~£>,87              -6.3$              -4.94              -3.95             -3.29 

as  the  motion  of  the  atmosphere  is  concerned.  The  function 
uniting  (Ql  -  Q)  -  k(q?-q*)  +  (R}+  (J)  being  unde- 
termined, it  is  very  difficult  to  make  satisfactory  progress  in 
this  direction,  and  the  problem  must  wait  for  further  develop- 
ments. Reviewing  columns  I  +  II  in  calories,  whiah  is  the 
heat  energy  available  from  the  temperature  distribution,  it  is 
seen  that  it  is  positive  and  diminishes  up  to  the  5000-meter 
level,  above  which  it  is  small  and  negative.  Comparing  this 
column  with  Tables  37  and  38  it  is  observed  that  the  vertical 
heat  potentiality  is  about  the  same  as  the  horizontal  capacity  for 
motion.  If  a  kilogram  of  air  is  moved  as  noted  by  the  condi- 
tions of  the  problem,  this  amount  of  heat  must  be  interchanged. 
In  the  actual  atmosphere  this  transfer  is  not  so  simple,  and 
hence  only  a  portion  of  the  Q-energy  is  actually  produced. 
How  much  less  is  really  generated  depends  upon  the  efficiency 
of  the  thermodynamic  engine  in  the  practical  physical  opera- 
tions of  the  air. 

TABLE  44. —  Valties  of  the  terms  in  the  formula, 

I  II 

C, n0(T-T)  +  Gp  T0  log  T0 (n,  -  n) 

=  (<?,-<?)-  i  (9,'-9')  +  R+  J- 
Energy  terms  in  the  horizontal  convection. 


FIG.  23. — Mean  values  of  the  gradient  ratio,  n,  at  the  cold  aud  warm 

maxima. 

The  computation  of  the  terms  I  =  Cp  «„  ( 2\  —  T)  and  11=  Cp  T0 
log  T0  (n,  —  n)  gives  the  results  that  are  found  in  Table  44, 
for  the  several  1000-meter  levels.  Term  I  is  positive  for  all 
levels,  and  term  II  reverses  the  sign  at  about  the  5000-meter 
level.  The  sum  I  +  II  is  reduced  to  calories  by  the  factor 
Am  =  0.0002389  in  Table  14.1  In  the  last  column  of  Table  44,  a 
mean  value  of  |  (q  *  —  q  02)  is  added  as  computed  by  Section  III, 
Table  43.  A  comparison  of  columns  4  and  6  shows  how  small 
the  velocity  term  is  in  comparison  with  the  heat  term.  An 
unknown  (R)  is  added  in  the  formula  to  represent  the  waste  of 
energy  in  passing  thru  friction  into  motion.  It  stands  be- 
tween the  energy  and  velocity  terms,  but  can  not  be  evaluated, 
and  it  is  presupposed  in  the  unexprest  function  that  connects 
heat  with  motion.  In  the  same  way  there  is  the  unknown 
radiation  term,  J,  wherein  some  heat  energy  is  wasted  so  far 


Height  in 
meters. 

I 

II 

I  +11 

I  +11  in 
calories. 

i  (?ls-9s) 

10000  

79.J6 

—90042 

-82106 

—  19.6 

113 

9000  

7946 

—67905 

—69959 

—  14.3 

129 

8000  

8394 

-66587 

—58193 

—  13.9 

134 

7000  

9443 

—74624 

—65181 

—  15.6 

126 

6000  

10909 

-80684 

—69775 

—  16.7 

98 

5000  

12571 

—38004 

—25433 

—    6.1 

75 

4000  

13509 

100427 

113936 

+  27.2 

58 

8000  

13830 

205529 

219359 

+  52.4 

55 

2000  

14921 

368533 

383454 

+  91.6 

30 

1000  

12971 

545913 

558884 

+138.5 

15 

0  

8252 

611771 

620023 

+148.  1 

11 

'See  Monthly  Weather  Review,  March,  1906,  page  115. 


SOME  CASES  OF  RESTRICTED  CONDITIONS. 

In  order  to  approach  this  intricate  problem  by  a  mathe- 
matical analysis,  it  will  be  desirable  to  study  some  simpler 
cases,  or  models,  wherein  the  conditions  are  limited  by  ideal 
restrictions.  These  consist  in  placing  two  masses  of  air  in 
adjoining  chambers,  or  in  one  chamber  with  a  movable  parti- 
tion, whereby  two  fixed  masses  under  given  conditions  when 
set  into  communication  react  upon  each  other.  Dr.  M.  Mar- 
gules  has  made  several  such  studies  in  his  paper,  Uber  die 
Energie  der  Sturme,  and  for  the  sake  of  profiting  by  this 
excellent  work,  I  have  prepared  a  brief  synopsis  of  the  results 
as  modified  by  myself  to  meet  nonadiabatic  conditions.  It  is  pro- 
posed to  give  the  assumed  data  and  the  resulting  formula, 
omitting  the  algebraic  reductions,  and  to  urge  that  the  student 
should  not  fail  to  read  that  paper.  In  order  to  preserve  the 
notation  of  my  formula,  the  following  table  of  equivalents  will 
be  useful: 


External  kinetic  energy 


Margules.     Bigelow. 

K  to  (i)—  i|  />  q1  d  u=i  m  q'. 


External  potential  energy 

Internal  kinetic  energy      ) 
Internal  potential  energy  j 


P  to 


=  Cp(- 


r   *         TJ- 

~ 


m  (molecules)  +  H,  (atoms)  ) 
JM  (molecules)  +  Ja  (atoms)  [ 


T    , 


Quantity  of  heat 


Work  of  expansion 


A  to-W=  _  Cdt  Cp  '  'rfu=  fa 
J      J   P  d  t          J 


567 


MONTHLY  WEATHER  REVIEW. 

Afargutes.     Bigelow. 
Potential  energy   +   centrifugal  force    W  to     Vt=  —  gr+%  w\ta\ 

Friction 


Velocity 

Volume 

Density 

Ratio  of  specific  heats 

Adiabatic  constant 

Height 

Surface 

Entropy  temperature 
Potential  temperature 
Drive  temperature 


(R)=  - 

c,  V  to  q 
k  to  v 
IL  to  /> 

•f    to       k=» 


1  to_*>_=sCp  =   (•/„ 

°k—  1~~R  =  7i~o0' 

c  to      h 

0  to       S 

9  to      T0 

T  to      T0 

.?  to      T0 

GENERAL    THERMODYNAMIC    EQUATIONS. 


Il  q  cos  (R  q) ,,  d  r. 


(1)     Conservation 
of  energy. 


Q=8U+3  W+  (R)  =  S(K) 


U  +  (R). 


Q  =  \ti(K)  +  SV]  external  +  [dH+  SJ]  internal  =  S  W+  5  U. 
External  work.  Internal  heat. 


(2)       Variation  of 
heat. 


dQ= 


(3)  External     po- 
tential energy. 


>—ST-*          +  ACpdT- 


in  mechanical  units. 


dQ=     pdv 


vdp  -\-  pdv 

~TS~ 


p" 


v= 


V  =Cp  dz+  (Z—z)  ph  =  RCTdm+  const. 

(4)  Internal  energy.   U=C»  CTdm+  const. 

(U+  F)=  (C0+R)  Crdm+  const.  =  OpCTdm  +  const. 

(5)  Transforma-  f    -<1(U+  V)=(U+V)a(imtial)-(U+V)e(&nal)=C]iC(T-Tl)d 

tion   of       J  ^ 

energy.  5 (.ff)  +  (^)  =  £  M?J  ==  C7pJ  ( T- Tl)dm=  Cp(T-  T1)  M. 

„  _   r^(?  T  v 

"t  I        rn    =    Cv  log    -fp    -f-    R    log    —  • 

*r       *  -ia  % 


(6)  Entropy  vari-  - 
ations. 


(7)  Potential  tem- 
perature. 


5S_1   dQ_OpdT      Rdp 
dz~  T  dz==~T  dz~  pfTz' 


^. 
P. 


DECEMBER,  1906 


(8)  In  linear  verti-        C  1 

exchanges.      J     Tdm  = 


(P.  T»  ~P 


DECEMBER,  1906. 


MONTHLY  WEATHEE  KEVEEW. 


568 


(9)  Auxiliary 
equations. 


nk 

T\'i^i 


Adiabatic. 

(7. 


k—l 


R 


1    RT 
-=-  pRT. 


Observed. 
nk         nCv 
1=1  ••      7? 

1  rfP 
•-,-  =  —  0- 


_ 

Rd 


fl  O 

0       ^_^  i7 

n         nC 


ldP 


CASE  i.  CHANGE  OF  POSITION  OF  THE  LAYERS  IN  A  COLUMN  OF  AIR.         Pf  TV  become  PJ,  T*,  and  the  function  must  be  integrated  thru- 

In  consequence  of  the  general  and  local  circulations  of  the     out  the  mass  M*'  the  temperature  of  the  mass  Mh  is  not  affected 

by  the  mutual  transfer  of  ml  J/2,  but  rises  or  falls  like  a  piston 
in  the  chamber,  while  its  lower  surface  maintains  the  pressure 
Ph.  Hence,  we  have  the  conditions, 


77Z/, 


JVto 


FIG.  24  A.      Initial. 


Final. 


atmosphere,  a  certain  gradient  a  =  —  prevails  at  a  given  lo- 
cality in  a  column  above  the  earth's  surface.  This  requires 
an  amount  of  heat  (?0  and  a  temperature  T0  at  each  level  zc 
to  maintain  the  stratum  in  equilibrium.  If  the  heat  energy 
changes  to  Q  for  any  reason  or  the  temperature  is  altered  to 
T  there  must  follow  a  change  in  elevation  to  z  to  restore  the 
equilibrium.  The  equation  of  equilibrium, 


(10) 


i  (9!-9o2)  =  (<?-<?„)  -  Cfn  ( T-  Tt) 

-Cfft]ogl'g(n-nt)-g(z-zt), 


is  available  for  the  computation  of  the  motion  due  to  stratifi- 
cations in  the  column.  In  order  to  take  a  simple  case  we 
assume  that  each  air  mass  retains  its  own  heat  energy  or  Q  =  Qa, 
and  that  the  gradient  is  the  same  thruout  the  column  or  n  =  n0. 
Hence  when  starting  from  rest  or  q  =  0,  the  equation  becomes 
for  the  unit  mass. 

(11)  £?'=  -Cfn(T-Tt)-g(z-zt). 

This  must  be  applied  to  each  mass  moved,  so  that  finally 


(12)       i 


-  Gp  n  (  T-  Tt)  -  g  (z  -  *„ 


Let  the  column  be  separated  from  the  surrounding  air  by 
walls  and  consist  of  four  parts.  M0  is  a  lower  section  not 
affected  by  the  transfer;  the  next  layer  m,,  under  pressure  Pl 
and  temperature  Tv  is  not  in  equilibrium,  so  that  the  stratified 
layer  m,  must  rise  if  T,  is  too  warm  and  fall  if  Tt  is  too  cold 
for  its  elevation  zt.  If  it  rises  thru  a  height  h  =  z2  —  z,,  and 
by  expanding  cools  to  a  given  temperature  T7/,  the  pressure 
P,  will  become  Ph  and  be  in  equilibrium  ;  the  section  M^  of 
thickness  h  falls  a  certain  distance  and  changes  its  tempera- 
ture; for  the  upper  differential  layer  d  l/2  the  initial  values 


Layer. 

AM 

m. 


Initial. 

7}        /TT 

T>        /TT 

k-l 


Final. 

P1  T1 

2    2      *  2 


Pressure. 


k—l 


T  > 

'  - 


k—l 


Substituting  in  the  equation, 


(15)  Kinetic  energy  =  Cp  [  f(  Tt  -  T,1)  d  m,  +  J"(  21,  -  T,1)  d  Jf,j  . 

(16)  Jm.g'- 


since 


*5  f lAf>  =  Cd^  =C^  =  h. 

PtJ     n    "    J  n/)^      J   n        n 


The  gravity  terms  in  these  equations  disappear,  because  the 
mechanical  work  in  each  case,  g  h  Ml  and  g  (Z3—Zlt)  Mt  ( where  Z^ 
is  the  height  of  the  center  of  gravity  of  Mt)  is  of  the  same  amount 
and  oppositely  directed.  Every  expansion  or  contraction  of 
air  masses  begins  on  an  adiabatic  gradient,  and  hence  the  for- 
mulas must  be  founded  on  that  basis.  But  minor  interchanges 
of  energy  as  heat  Q  and  velocity  J^2  almost  immediately  begin 
in  the  mixing  process,  so  that  the  theoretical  conditions  soon 
suffer  modifications  which  it  is  quite  impracticable  to  follow 
out. 

CASE  II.     THE  TEMPERATURE  IS  A  CONTINUOUS  FUNCTION  OF  THE  HEIGHT, 

T^T-ah. 

It  is  important  to  eliminate  the  pressures  from  the  formula 
and  express  the  function  in  terms  of  g,  h,  T,  and  the  gradients. 
Several  forms  of  the  function  for  the  temperature  distribution 
may  be  employed  to  represent  the  atmosphere,  but  it  is  only 
occasionally  that  these  formulas  can  be  used  to  replace  the 
actual  pressure  and  temperature  observations  at  different  lev- 
els. For  the  observed  gradient  we  have 

(18)    Observed 
gradient. 


569 

Hence, 

(19)      Adiabatic 
gradient. 


(20) 


(21) 


MONTHLY  WEATHER  REVIEW. 


DECEMBER,  1906 


ah\' 
TJ 


K 

*    "    =    l~ 


ah\9jCa 
'TJ 


CASE  III.  FOR  LOCAL  CHANGES  BETWEEN  TWO  ADJACENT  STRATA  OF  DIF- 
FERENT TEMPERATURES,  WHERE  ON  THE  BOUNDARY  THE  PRESSURE 
P  =  P,1  =  P,1,  AND  THE  TEMPERATURE  IS  DISCONTINUOUS. 


Then, 


Finally, 


Take  the  following  conditions: 


+  i  .  a-fl 

O    J 


iyer. 

Initial. 

Final. 

m, 

P2T2 

P  l  T  ] 
a  a 

m, 

p,r, 

P  l  T  * 
1  1 

Pressure. 


P,1 


Temperature. 


7"-T 
~       ' 


k-1 
nk 


The  equation  of  equilibrium  becomes,  for  P>l=Pl^= 


(23) 


The  mass  m,  is  driven  from  its  position  with  a  velocity- 
energy  inversely  proportional  to  the  temperature,  so  that  warm 
air  has  less  driving  power  than  cold  air.  The  drive  depends 
upon  the  departure-ratio  n  and  vanishes  when  n=l,  that  is, 
for  an  adiabatic  expansion  in  an  adiabatic  gradient.  When 
a  >  ac  the  mass  ml  is  in  unstable  equilibrium-  —  is  too  cold  for 
its  position  and  tends  to  fall.  Example,  for  w=0.5,  <z=19.74> 
oc=  9.87.  When  a<ao  the  mass  ml  is  in  stable  equilibrium. 
Example,  for  n=  2,  a  =  4.94  <  a  0=  9.87  It  is  not  possible  to 
drive  the  small  mass  m,  thru  any  great  height  h  in  the  atmos- 
phere, because  the  differential  energy  in  the  expanding  mass 
sets  up  minor  whirls  which  tend  to  interchange  the  Q-energy 
by  mechanical  effects  and  internal  friction. 


energy 


Since        J= 


\.m.Ss(T—T), 

?  m  g   /I  __  1  \ 

1  *  n  \/oj    /y 

and  — — -3  =    ,  therefore 


i 
The  result  is  to  change  the  gradient  from  a0  to  a  = 


If 


(24) 


n    Pi  Pi 
The  kinetic  energy  inducing  an  interchange  is  proportional 


the  displacement  of  the  mass  m  t  takes  place  in  the  medium  of 

gradient  a  then  the  drive  may  be  exprest  by  terms  of  the  form, 

to  the  difference  of  the  densities  and  inversely  proportional  to 

the  product  of  the  densities.     Hence,  if  strata  of  different 
densities  are  flowing  over  one  another  in  the  general  circula- 
where  n  l  is  the  effective  ratio  of  the  moving  mass  m  1  and  a     tion  which  is  temporarily  stratified,  these  two  strata  tend  to 


(22) 


n  —  n 


that  of  the  prevailing  general  gradient. 


mix  by  interpenetration  according  to  this  law. 


AUXILIARY    THEOREM.       EVALUATION    OF  f  T  d  m    IN    LINEAR   VERTICAL    TEMPERATURE    CHANGES. 


(25) 


Assume   T  =  T0-  a  z, 


P=p(^\glRa,  fTdm  =    C  T  ,,  d 


000  0 

Change  the  limits  of  integration  from  z  to  T. 


(26) 


(27) 


d  z 


=  —  -  CTX  d  T. 
a  J 

rpo 


T=T^-az,      dT=-adz,       -±dT-4*. 

(Tpdz=  .I  P  T  ~^«  fV'^dr-  --P  T~9l**[T°-—  -  T9I>'°+1] 

*}  Ha      oo          ^/  jfd     e    o          |^i_|_p|  jta 


IRa 


Ra 


(Pt  T0-P  T). 


For  any  gradient  other  than  the  adiabatic  we  have, 


(28) 


1+ 


nk 


DECEMBER,  1906. 


MONTHLY  WEATHER  REVIEW. 


570 


CASE  IV.    THE  OVERTURN  OF  DEEP  STRATA  IN  THE  COLDMN. 

Let  the  pressures,  temperatures,  and  heights  be  arranged 
in  the  initial  and  final  states  as  indicated  in  the  diagrams  (fig. 
24  B).  The  greatest  entropy  in  1  is  less  than  the  least  in  2, 
so  that  the  cold  mass  1  will  fall  beneath  the  warm  mass  2. 
The  heights  of  the  masses  will  change  as  well  as  the  pressures 
and  temperatures. 

Assume  P0,  T02,  h},  T{l,  hv  as  known  in  the  initial  state. 


Tr, 


h.f 


A 


Pressures. 


(29) 
(30) 


Temperatures. 


ria=roj- 


P  /r*A 

{  IT^-J 
\-*<  i  / 


nk 
t-1 


-  T 
~          ~ 


iCooV 


Ft    Tiz 


2'Wa 

-pf      rp' 

-ti    yz.2 


Fl   Tl, 
1  Cool> 

TO  rjr' 

-£o        J-  Ot 


/nttia/ 


rinef 


FIG.  24  B. 


Substitute  in  Gp  (  Cldm  —  CT1dml  j  successively. 

(31)      Initial,  ( V  +  U)a  =  Cp  (Td  m  =  2z  -  -1—-  (P.  Tm  -  Pi  Tit  +  Pt  Ttl  -  Ph  Thl)  +  const. 

"  "   1  +    — 


(32)      Final,     (V+l')e  = 


nk 


T   (P.  TK  ~  pi  Titl  +  P^  ZV  -  Ph  T^)  +  const. 

9    1  +  / 

nk 


(33)  Kinetic  energy      =  (F+  E7)0  —  (F+  U)e  =  \  M  q2  =  \ 

(34)  Heights,  A1'=^(T01'-Til'),  V=  ^  (T 

(35)  Approximate  solution  of  Case  IV.  \  (f  =        -r- 


A     3s- 


^-l-  h  T- 


CASE  V.      TRANSFORMATION  OF  TWO   MASSES  OF  DIFFERENT  TEMPERATURES  ON  THE  SAME  LEVEL  INTO  A  STATE  OF  EQUILIBRIUM. 

TA  Tfa 


T*,           P*,          T»z 

21 
Ti, 

hl 

Poi          7oi 

Pn      To, 

Pi         j,         Ti, 
Fo                     To 

J3, 

/nifial 

FIG.  24  C. 

Given  as  data  at  the  height  h,  Thl,  Thi  Ph,  the  areas  jB,,  Bv  the  entropy  #,  <  Sf     Hence  by  the  formulas, 

nk  nk 


(36)  Pm=Ph(j 

(o7)   Pm  =  P /,  I  ip     I 

(38)    Initial.     (  V+  U)a=  Cp 


gh 


l  -    -^-^  B 

9  i   i    _  _  ±  " 
nk 


(39)    P\  =Ph 


-  Ph). 


(Pn  Tot  —  Ph  Thl  +  Pu  T0)  —  Ph  Th2)  +  const. 


(Pn  ~ 


(40)    Final.       (T^+  U).=  Cp  l  -  T  B(P\  T\-P\  T\  +  P\  T\,-Ph  Th})  +  const. 

Q    t     .    #       J- 


9  1  + 


nk 


(41)  Kinetic  energy.     \  M  <?  =  (  V  +  U),  —  (  V  +  U)e     . 

(42)  Mass  and  heights.     M=  B  (P\—Ph).         h\  =  ^ 


h\=     »(2"4f—  Tht). 


571 


MONTHLY  WEATHER  REVIEW. 


DECEMBER,  1906 


(43)  Approximate  solution  for  Case  V.      Take  7  =  T>      T>.        T'  =  T,  Tf  M=  BPh  £     =  B  ,>  h  (approximate). 

(44)  i  MY  =  \M.    ' '     «ff  fcr. 


(45)  Assume 
(46) 

(47) 

(48)  T, 


CASE  VI.        CONTINUOUS  HORIZONTAL  TEMPERATURE  DISTRIBUTION    WITH  ADIABATIC  VERTICAL  GRADIENT. 

A,  &  & 


Co 

>t 

Fr 

* 

Fox 

Initial 


ELnat, 


FIG.  24  D. 


f(Pal-Ph)dx  =  P-\P-Ph-}    hp^-P^dx]. 
I  J  I  J 

l-x  l-x 


T-  T>=  T-  T  = 


z. 


*=  Cp  J"(T~  T>) 


lPh 


(50) 
(51) 


CASE  VII.  POSITION  OF  LAYERS  OF  EQUAL  ENTROPY  WHEN  THE  PRESSURE 
AT  A  GIVEN  LEVEL  IS  CONSTANT  AND  THE  TEMPERATURE  AT  THIS  LEVEL 
IS  A  FUNCTION  OF  THE  HORIZONTAL  DISTANCE  AND  A  LINEAR  FUNCTION 
OF  THE  HEIGHT. 

Let  the  gradient  ratio  which  distinguishes  one  stratification 
of  the  air  from  another  having  a  different  temperature  gra- 
dient be  n. 


(52)  P  =  f 

(53)  The  curves.  F(xz)=n  log  Tk—(n—l)log  T=  const. 

(54)  Angle  of  d  F Id  F         n 


TM.                         Th, 

111 

s 

r, 

T 

2 

1 

2 

i 

i 

TV                                          to! 

-2'- 


curves. 


(56)      Entropy^ 


Initiai  EinaL 

FIG.  24  E. 

,  =  Cp  [n,  log  Thl  -  (n,  -  1)  log  TJ  +  const 


^C,,  (n,  log  7',2  -  (n,  -  1)  log  71,)  +  const. 


CASE  VIII.    FINAL  CONDITION  OF  TWO  AIR  MASSES  UNDER  CONSTANT  PRES-       (  57 )  \Og  -jjf  __    JQ         ?s_ 

SURE  WITH  GIVEN  INITIAL  LINEAR  VERTICAL  TEMPERATURE  FALL.  Z7,    ~  '     Th , 

On  removing  the  partition  the  layers  1  and  2  spread  out, 
change  their  heights,  and  there  is  a  mixed  stratum  between 
them.  (58)  Heights 


n 
n  —  1 


•_/.* 
\, 


( 55 )     Temperatures 


9 


If  the  vertical  temperature  fall  of  the  masses  1  and  2  is 
smaller  than  in  adiabatic  equilibrium,  then  the  entropy  in- 
creases with  the  height,  and  it  can  happen  that  in  the  colder 


DECEMBER,  1906. 


MONTHLY  WEATHER  REVIEW. 


572 


mass  (1)  the  entropy  at  the  height  A,  will  be  as  great  as  in  the 
warmer  mass  (2)  at  the  ground.  The  higher  layers  in  (1)  form 
a  series  with  an  entropy  equal  to  the  layers  in  (2)  up  to  the 
height  h  —  hr  In  the  final  state  the  under  part  of  (1)  will 
spread  out  on  the  ground,  above  it  will  be  layers  which  are 
mixtures  of  (1)  and  (2),  and  farther  up  will  lie  the  masses  of  (2) 
which  initially  were  between  (h  —  ht)  and  h.  On  the  bounda- 
ries of  the  three  layers  the  temperature  transition  is  continu- 
ous. 

It  will  be  convenient  to  approach  the  dynamic  equations  of 
motion  in  cyclonic  vortices  thru  a  study  of  the  Cottage  City 


waterspout  of  August  19, 1896.  It  should  be  recognized  that 
in  ordinary  cyclones  the  vortices  are  not  perfect  and  it  is  only 
rarely  and  in  highly  developed  storms  that  anything  like  pure 
vortex  motion  is  attained.  The  waterspout,  therefore,  offers 
a  good  example  of  vortex  motion  in  the  atmosphere  with  which 
to  test  the  above  equations.  I  may  remark  that  the  theory 
first  advanced  in  my  International  Cloud  Report,  1898,  for  the 
generation  of  cyclones  and  anticyclones  in  the  general  circu- 
lation seems  to  be  practically  confirmed  by  these  studies  based 
upon  actual  observations. 


JULY,  190(5. 


MONTHLY  WEATHER  REVIEW. 


307 


STUDIES  ON  THE  THERMODYNAMICS  OF  THE   ATMOS- 
PHERE. 
By  Prof.  FRANK  11.  BIUELOW. 

VI.— THE   WATERSPOUT   SEEN   OFF  COTTAGE    CITY,  MASS.,  IN 
VINEYARD  SOUND,  ON  AUGUST  19,   1896.1 

THE    SOURCES    OF    THE    DATA    USED    IN  THE    DISCUSSION. 

This  waterspout  has  an  especial  scientific  interest  for  mete- 
orologists because  it  was  seen  under  circumstances  remarkably 
advantageous  for  making  observations  and  photographs,  from 
which  it  is  possible  to  compute,  with  much  accuracy,  the 
dimensions  of  the  tube,  and  thus  facilitate  the  application  of 
the  mathematical  theory  of  vortices. 

A  series  of  papers  and  letters  from  various  persons  who  saw 
the  phenomenon,  and  a  very  complete  set  of  photographs,  were 
secured  at  the  time  by  the  Editor,  which  he  has  courteously 
placed  at  my  disposal  for  incorporation  in  this  paper,  and  they 
will  be  found  inserted  in  the  following  pages.  I  have  myself 
been  familiar  with  that  part  of  the  Massachusetts  coast,  and 
have  therefore  been  interested  to  study  the  facts  as  thoroughly 
as  possible,  as  a  preliminary  to  the  discussion  of  this  type  of 
vortex  motion.  I  accordingly  visited  Cottage  City  the  follow- 
ing September,  and  was  conducted  by  Mr.  Chamberlain  to  the 
spot  where  he  placed  his  camera  for  making  his  photographs. 
There  I  made  a  sufficiently  accurate  survey  of  the  linear  dis- 
tances between  that  spot  and  the  telegraph  poles  shown  in  his 
pictures  to  determine  the  scale  of  distances  for  all  objects. 
Furthermore,  by  collecting  and  collating  all  the  data  relative 
to  the  positions  of  the  waterspout  and  the  schooner  seen  in 
the  several  photographs,  I  am  able  to  plot  them  on  the  Coast 
and  Geodetic  Survey  Chart  No.  112,  in  such  a  way  as  to  recon- 
cile nearly  all  of  the  statements  made  regarding  the  distances 
and  progress  of  the  two  objects,  respectively.  The  photo- 
graphs taken  from  such  distances  as  Vineyard  Haven  and  Fal- 
mouth  Heights  give  an  excellent  view  of  the  whole  cumulo- 
nimbus cloud  from  which  the  tube  descended,  and  its  connec- 
tion with  the  thunderstorm  which  preceded  it.  All  these  data 
will  enable  us  to  discuss  the  subject  of.  tornado  and  waterspout 
formation  with  considerable  fulness,  and  with  the  conviction 
that  confidence  may  be  placed  in  the  comparison  of  the  obser- 
vations with  computations.  There  is  every  reason  to  believe 
that  the  photographs  are  perfectly  genuine,  and  free  from 
touches  to  add  to  their  artistic  beauty  at  the  expense  of  scien- 
tific accuracy.  Certain  preliminary  computations  were  made 
in  18!)7,  the  result  of  which  was  published  in  the  International 
Cloud  Report,  page  633,  Report  of  the  Chief  of  the  Weather 
Bureau  1898-99,  Volume  II;  this  was  republished  in  the 
MONTHLY  WEATHER  REVIEW.*  My  purpose  then  was  to  illustrate 
the  application  of  certain  formulas,  and  it  was  my  intention  at 
that  time  to  complete  the  study  as  soon  as  my  other  duties  per- 
mitted. In  these  present  papers  I  shall  begin  with  the  descrip- 
tive accounts  of  the  waterspout,  then  pass  to  a  discussion  of 
the  facts  as  shown  by  these  reports  and  the  photographs,  and 
finally  consider  the  dynamic  motions  and  the  thermodynamic 
conditions  present  in  the  atmosphere  near  Cottage  City  on 
that  occasion. 

r.ETTF.RS    AND    REPORTS    OF    OBSERVERS. 

The  following  letters,  reports,  and  observations  have  been 
furnished  by  the  several  authors.  It  will  be  instructive  to 
refer  to  fig.  25  while  reading  these  papers. 


(A)    IC.XTHVI.T  HiCIM  THE  DAILY  JOURNAL  OF   U.   S.    WEATHER   BUREAU  STATION,    VlNE- 

YARD  HAVEN,  MASS.,  W.  \V.  NEIFERT,  OHSERVER. 

Auyiist  W,  7,s'.%'.— Partly  cloudy  weather  during  the  morning,  with 
gentle  northerly  wind.  Three  magnificent  waterspouts  were  observed  in 
Vineyard  Sound  to-day,  in  northerly  direction  from  station,  about  ten 
miles  distant.  During  the  entire  afternoon  the  weather  was  partly 
cloudy  and  sultry,  with  groat  masses  of  cumulus  clouds  in  the  north  and 
northeast.  At  1.1:45  the  first  display  was  observed.  At  first  a  long  spiral 

1  Xo.  V  of  the  series  ("  The  Horizontal  Convection  In  Cyclones")  will 
follow  later. 
'May,  1902.     Vol.  XXX,  pp.  257,  258. 


column  seemed  to  fall  from  the  clouds,  about  the  thickness  of  a  man's 
body,  but  this  gradually  increased  in  size  as  the  cloud  lowered,  and 
when  it  reached  the  water  it  was  as  thick  as  a  large  sized  cask,  and 
changed  in  color  from  a  rich  gray  to  a  black,  and  assumed  a  funnel 
shape  at  the  base  of  the  clouds.  The  cloud  seemed  of  a  yeasty  white 
where  the  column  came  in  contact  with  it,  and  looked  as  though  the 
water  was  hauled  up  to  it.  The  area  of  contact  appeared  small.  The 
spout  was  very  straight  and  almost  perpendicular,  kicking  up  a  great 
sea  as  it  traveled.  When  it  disappeared  it  began  to  do  so  at  the  base 
and  rapidly  reached  the  top,  having  the  appearance  of  clouds,  and 
finally  cleared  away,  like  steam  from  an  engine,  at  12:58  p.  m.,  leav- 
ing a  clear  sky  for  a  background  and  the  original  clouds  above.  At 
1  p.  m.  it  formed  the  second  time,  which  was  really  the  most  interesting 
spectacle  of  all.  From  a  mass  of  inky  clouds  it  reached  down,  finger- 
like,  to  almost  the  ocean's  surface.  Below  it  the  water  was  stirred  to 
an  angry  whirlpool,  the  foam  reaching  up  perhaps  a  hundred  feet.  It 
appeared  as  though  great  volumes  of  water  were  traveling  up  to  the 
cloud  by  an  endless  screw,  when  suddenly,  at  1:18  p.  m.,  the  long  arm 
disappeared  in  a  manner  similar  to  the  first.  At  1:20  it  formed  for  a 
third  time  and  scarcely  reached  the  water,  but  had  a  decided  funnel  shape, 
lasting  about  five  minutes,  when  it  slowly  withdrew  into  the  blackness 
above  and  the  surface  of  the  ocean  became  quiet.  There  was  a  sprinkle 
of  rain  from  12:54  to  1  p.  m.,  amounting  to  a  trace.  During  the  display 
the  wind  at  the  station  was  six  milt- s  per  hour  from  the  northwest;  tem- 
perature 72°,  with  a  fall  to  56.5°  during  the  thunderstorm  which  fol- 
lowed, passing  ov<*r  the  station  from  northwest  to  south.  Thunder  was 
first  heard  at  1:45  p.  m.;  loudest  at  3:04  p.  m.;  last  at  3:45  p.  m.  Heavy 
downpour  of  rain  from  3:04  to  3:15  p.  m.,  then  continued  light  rain  until 
3:30  p.  m.  Amount,  0.38  inch.  The  summer  residents  were  stricken 
with  fear  at  the  approach  of  the  dark  clouds  over  the  sound,  and  viewed 
the  waterspout  with  mingled  feelings  of  awe  and  interest.  It  was  a 
sight  long  to  be  remembered,  and  when  the  weather  cleared,  about  4 
p.  m.,  each  expressed  himself  as  being  most  fortunate  in  having  es- 
caped some  dreadful  calamity.  No  noise  was  heard  here,  but  the 
sehooner-yacht  Avalon  of  Boston  was  very  near  the  spout  aud  those  on 
this  vessel  reported  plainly  hearing  the  noise  and  the  wind  blowing  around 
the  vortex  with  wonderful  rapidity;  to  them  the  spout  appeared  to  be  one 
hundred  feet  in  diameter.  The  three  spouts  moved  gracefully  to  the 
eastward.  This  is  the  first  display  of  this  phenomenon  witnessed  here 
for  27  years.  Mariners  hero  who  have  circled  the  globe  a  number  of 
times,  and  have  seen  dozens  of  waterspouts,  declare  it  to  be  the  most 
perfect  specimen  they  ever  observed. 


(B)  LETTER  FROM  MR.   NKIFKRT  TO  MR.   A.   J.   HKNRV.     DATKD  VINEYARD  HAVEX, 
MASS.,  DKCKMIIKII  19,  1896. 

When  I  first  saw  the  waterspout  it  was  in  the  vicinity  of  Black  Buoy 
No.  13,  on  the  east  end  of  L'Hommedieu  Shoal.  Can  not  say  now  ex- 
actly, but  in  that  general  direction.  Oould  just  sec  base  off  East  Chop. 
When  the  photographic  view  was  taken  here  it  was  about  where  the  red 
dots  surround  sounding  marked  8i.  It  appeared  nearer  then,  but  I  pre- 
sume this  was  caused  by  its  base  being  hidden  by  the  "highlands".  The 
view  from  here  was  taken  from  on  board  of  a  yacht  which  lay  at  the  red 
dot  between  the  two  wharfs  or  the  head  of  the  harbor  under  the  figure 
3  of  the  sounding  marked  13.  *  It  may  not  be  so  far,  but  that  is  as  I 
remembered  it.  There  was  so  much  confusion,  women  and  children  cry- 
ing, that  I  was  not  very  observant  until  it  was  over. 

Coolidge  was  just  north  of  the  head  of  the  wharf  in  Cottage  City,  and 
the  "spout  "was  in  an  east-northeast  direction  from  him.  His  views 
were  made  from  the  same  position,  and  only  time  enough  elapsed  be- 
tween them  to  change  the  plates. 


(€)  EXTRACT  FROM  THE  DAILY  JOURNAL  OF  THK  U.  S.  WEATHER  BUREAU  STATION, 
NANTUCKET,  MASS.,  MAX  WACXEK,  OIISEKVEK. 

August  19,  1896.— Clear  weather  all  day,  except  in  the  afternoon,  when 
light  rain  began  at  2:40  p.  m.  and  ended  at  4  p.  m.  Total  amount  0.03 
inch.  Cooler,  with  rising  barometer.  Mr.  Wagner  went  to  Cottage  City 
in  the  morning  to  check  up;  from  there  he  observed  the  big  waterspout 
that  formed  in  Nantucket  Sound.  An  ordinary  thundershower  was  pass- 
ing across  the  sound  when,  about  12:40  p.  m.,  a  huge  black  tongue  shot 
down  from  an  alto-cumulus  cloud  that  floated  a  half  mile  high  at  the 
northern  edge  of  the  shower,  and  after  rising  and  falling  a  number  of 
times,  finally  joined  a  shorter  tongue  that  seemed  to  leap  out  of  the 
water  to  meet  it.  Twice  the  column  parted  for  a  moment,  but  joined 
again  instantly.  There  was  no  apparent  motion  of  the  waterspout  for- 
ward, and  the  phenomenon  lasted  for  half  an  hour.  It  was  pronounced 
by  many  sea  captains  who  witnessed  it  the  finest  waterspout  they  had 
ever  seen.  No  damage  was  done  by  the  spout,  but  a  small  catboat 
which  arrived  at  night  reported  being  becalmed  near  the  spout,  the  crew 
being  badly  scared. 


(D)    EXTRACT  FROM  THK  DAILY  JOURNAL,  U.  S.  WEATHER  BUREAU  STATION,  WOODS 
HOLE,  MASS.,  J.  D.  BLAODKX,  OBSERVER. 

August  19,  1896.— Three  waterspouts  were  reported   in  the  Vineyard 
3  On  chart  not  reproduced. — EDITOR. 


3UH 


MONTHLY  WEATHER  REVIEW. 


JULY,  1906 


EAST     FALMOUTH 


HAMLIN      PT. 
GUMrllMG    PT. 


SUCCOHESSE.T  PT 


FALMOUTH 
>*EIGIHT 


QUAMOUISSET 


5UCCONESSET     -SHOAL 

LIGHT-SHIP     * 


nOriAMESSET 


VIMEYAR.D    HA 


EDQARTO 
R  LISHT 


SCALE  OF  MILES 

-3 


KILOMETERS 


KATA.MA 
BAY 


FIG.  25.— Location  of  waterspout  seen  In  Vineyard  Sound,  August  19,  1896.    (Reduced  from  United  States  Coast  and  Geodetic  Survey  chart  No.  112.) 


JULY,  1906. 


MONTHLY  WEATHER  KEVIEW. 


309 


being  generally  accompanied  with  flashes  of  lightning  and  a  sulphurous 
smell  showing  the  activity  of  the  electrical  principle  in  the  air. 


FIG.  26. — Diagram  of  the  survey  between  site  of  Chamberlain's  camera 
and  four  telegraph  polos  shown  in  his  photograph,  2d  A  (fig.  27). 


Sound  and  one  in  Buzzards  Bay  between  12:35  and  2  p.  m. 
spout  was  photographed  with  excellent  results. 


One  water- 


COPY  OF  \  CIRCULAR  ACCOMPANYING  COPYRIGHT  PHOTOGRAPHS. 
BERLAIN,  OP  COTTAGE  CITY,  MASS. 


BY  J.  N. 


About  12:45  noon,  August  19,  1896,  we  were  startled  by  the  cry  of  "  A 
waterspout  !  "  and  wit  h  our  assistants  started  with  the  camera  to  the  park 
in  front  of  Doctor  Tucker's  residence,  where  we  could  see,  a  little  north 
of  the  direction  of  Nantucket,  very  dark  and  angry  clouds,  out  of  which 
a  funnel-shaped  cloud  of  various  colors,  with  a  pointed  streak,  issued 
downward  until  it  touched  the  water.  We  obtained  two  photographs  of 
this,  showing  a  slight  difference.  [One  of  these  views  is  reproduced 
as  fig.  27.]  After  about  twelve  minutes  it  gradually  and  completely 
vanished.  Very  soon  a  second  one  appeared,  more  curved  than  the 
first,  with  a  long  sharp  streak  from  the  same  clouds  and  slowly  extend- 
ing downwards  to  a  point  about  one  hundre'd  feet  from  the  surface 
of  the  ocean.  In  a  few  moments  this  changed  to  a  smaller  streak  with 
a  different  curve  bending  to  the  south,  while  the  former  bent  to  the 
north.  Both  of  these  we  photographed  [figs.  34,  35].  The  height  of  this, 
which  Professor  Dwight  of  Vassar  College  says  was  a  genuine  waterspout, 
was  about  a  mile.  The  cloud-burst  disturbed  the  water  in  the  sound 
for  several  hundred  yards  until  it  looked  like  a  boiling  pool.  We  could 
trace  through  the  camera  the  spiral  motion  of  the  water  as  it  was  drawn 
into  the  clouds,  every  moment  augmenting  their  portentous  darkness. 
The  cloud  from  above  and  the  spray  from  below  were  drawn  together  by 
suction,  and  condensed  torrents  of  water  poured  down  a  few  hours  later, 
which  was  found  by  persons  in  different  places  on  the  island  to  be  salt, 
and  proves  that  it  was  can  led  up  to  a  height  and  scattered  round  as 
solid  bodies  are  by  tornadoes  on  land.  The  Greeks  applied  the  term 
"prester"  to  the  waterspout,  which  signifies  aflery  fluid,  its  appearance 


(F)     A    REPORT  TO  THE    EDITOR  BY    PROF.    W».    B.    DWIGHT,  VASSAR  COLLEGE,  POUOH- 

KEEPSIK,  N.  Y.    DATED  MARCH  22,  1897. 

I  now  inclose  such  statements  as  I  am  able  to  make  without  the  few 
memoranda,  noted  on  the  spot  and  since  lost,  of  the  waterspout  of  last 
summer  at  Cottage  City. 

The  basis  of  my  estimates  of  the  height  of  the  waterspout  is  rather 
hypothetical,  but  I  submit  them  for  what  they  may  be  worth.  I  have 
endeavored  to  assume  my  units  of  measurement  so  as  to  be  below  rather 
than  above  the  fact,  in  order  that  the  estimate  might  not  seem  to  be  made 
in  a  spirit  of  exaggeration.  Thus,  I  am  inclined  to  think  that  the  dis- 
tance of  the  schooner,  in  the  photographs,  from  the  shore  is  nearer  three 
than  four  miles,  which  would  make  the  spout  higher  than  my  estimate. 
One  reason  for  my  thinking  so  is  that  there  is  a  buoy,  the  three-mile  buoy, 
so  called,  not  far  from  the  position  of  the  schooner  and  in  front  of  her, 
about  three  miles  from  the  shore  and  marking  the  channel.  She  was 
likely  aiming  for  that  buoy  and  then  .would  not  be  very  far  from  it.  On 
the  other  hand,  the  state  of  the  wind  might  lead  her  to  go  as  much  as 
half  a  mile  or  more  outside  (to  the  east)  of  it.  I  presume  that  the  opinion 
of  the  seamen  at  Cottage  City  on  the  distance  of  the  schooner  could  be 
easily  obtained  and  would  be  of  value.  I  think  that  I  obtained  such  an 
opinion,  but  it  is  lost  with  my  other  memoranda  and  I  can  not  now  recall 
it.  I  have  searched  for  the  three-mile  buoy  in  the  photographs,  but  it 
is  a  very  small  object  and  I  cannot  identify  it. 

Some  statements  as  to  the  waterspout  in  Nantucket  Sound  (sometimes  called 
Vineyard  Sound)  easterly  from  Cottage  City,  Marthas  V-neyard,  Mass., 
at  noun  of  August  19,  1896,  made  from  personal  observations  by  William 
B.  [Height,  of  Vassar  College,  Poughkeepste,  N.  Y.  (resident  vn  the  summer 
at  Cottage  City). 

My  summer  cottage  is  situated  close  to  the  beach  at  Cottage  City,  with 
unobstructed  view  of  the  ocean.  I  was  standing  upon  my  private  wharf, 
nearly  in  front  of  the  cottage,  when  the  waterspout  of  August  19,  1896, 
began;  I  saw  it  at  the  outset  and  was  among  the  first  to  call  general  atten- 
tion to  it  in  our  part  of  the  town.  I  watched  it  closely,  with  the  assist- 
ance of  a  good  field-glass  till  the  close  of  the  phenomenon,  but  I  had  no 
proper  instrument  at  my  command  for  taking  the  altitude. 

Excellent  photographs  were  taken  by  Mr.  Coolidge  and  Mr.  Chamber- 
lain. I  am  able  to  testify  to  their  general  correctness  as  corresponding 
with  personal  observation.  Mr.  Coolidge's  are  most  artistic  views  of  the 
whole  scene  and  scenery.  Three  of  Mr.  Chamberlain's  present  with  accu- 
racy three  consecutive  views  of  the  waterspout  in  its  phases,  changes,  and 
progress  taken  from  one  and  the  same  spot.  They  were  taken  with  total 
disregard  of  the  foreground  and  the  sole  aim  of  getting  the  best  views 
of  the  spout  itself.  These,  facts  give  these  three  views  a  marked  scien- 
tific value,  and  these  photographs  will  repay  a  careful  scientific  study. 

Like  all  of  the  three  phenomena  of  this  kind  which  I  have  personally 
observed  (and  this  is  the  second  which  I  have  seen  from  Cottage  City), 
the  funnel  of  the  tornado  is  constantly  changing  its  form,  length,  and 
other  dimensions;  and  occasionally,  or  at  intervals,  it  may  entirely  dis- 
appear in  its  cloud,  only  to  reappear  again  in  full  force.  This  one  had 
several  such  successive  appearances  with  intervals  of  total  disappear- 
ance. Hence  the  photographer,  the  newspapers,  and  the  spectators  gen- 
erally described  the  appearance  of  several  waterspouts  on  this  occasion. 
I  consider  this  an  unscientific  and  unfortunate  mode  of  describing  this 
phenomenon,  chiefly  for  these  two  reasons. 

1.  There  was  only  one  great  but  entirely  distinct  and  Individual  cloud 
concerned  in  the  phenomenon  from  beginning  to  end,  and  in  fact  only 
one  particular  spot  in  that  cloud.     This  not  only  follows  from  my  own 
observation  but  is  demonstrable  from  a  study  of  Chamberlain's  three 
photographs,  as  I  propose  later  to  show.     This  cloud  and  its  point  of 
vortex  movement  sustained  constantly  throughout  the  waterspout  phe- 
nomenon, three  quarters  of  an  hour  (or  more),  the  same  relation  to  the 
furious  squall  of  lightning,  thunder,  rain,  and  hail,  going  on  about  a  mile 
to  the  southeast  of  the  waterspout,  i.  e  ,  a  mile  from  the  thunderstorm 
to  the  edge  of  the  waterspout.     This  squall  is  clearly  visible  In  Cham- 
berlain's first  photograph  of  the  three  mentioned. 

2.  From  the  point  mentioned  in  the  tornado  cloud,  (as  I  will  designate 
it  in  distinction  from  the  squall  cloud),  a  watei spout  funnel  would  de- 
scend to  the  ocean,  and  move  along  its  surface  in  an  easterly  direction, 
with  its  cloud;  after  a  while  it  would  thin  out,  or  break  into  pieces,  and 
nearly  or  quite  disappear.     For  the  most  part,  however,  the  location  of 
its  minimized  force  in  the  cloud  remained  marked  clearly  by  a  downward 
bulging  of  that  part  of  the  cloud,  with  indications  often  of  rotary  move- 
ment at  the  spot.     Once,   however,  the  spot  where  this  tendency  to 
vortex  motion  still  existed  was  for  a  few  minutes  lost  to  view;  but  soon 
the  vortex  movement  visibly  returned  somewhere  along  the  line  between 
the  cloud  and  the  ocean,  from  the  point  of  the  cloud  which  was  affected. 
It  generally  appeared  first  at  the  cloud,  but  once  the  vortex  movement 
at  the  ocean's  surface  was  practically  simultaneous  with  that  at  the 
cloud;  then  another  column  or  spout  was  completely  formed,  but  as  the 
cloud  had  been  moving  eastward  during  the  interval,  the  spout  would 
of  course  be  seen  in  a  position  somewhat  to  the  eastward  of  its  former 
place;  and  so  this  disappearance  and   reappearance  was  several  times 


310 


MONTHLY  WEATHER  REVIEW. 


JULY,  1906 


repeated.  Those  of  the  more  intelligent  observers  who  insist  that  there 
wore  "several  waterspouts"  ou  this  occasion  base  their  statement  on 
these  two  arguments:  (1),  that  there  were  successive  spouts  seen;  (2), 
that  no  two  of  the  spouts  were  in  the  same  place. 

On  tho  contrary,  I  hold  that  my  preceding  remarks,  and  the  further 
facts  to  which  I  shall  call  attention  later,  show  that  this  was  tho  same  phe- 
nomenon, that  is,  the  same  center  of  vortex  action,  throughout,  and  that 
its  different  appearances  were  not  different  waterspouts,  but  simply  dif- 
ferent and  varying  phases  of  one  and  the  same  phenomenon.  As  to  the 
second  point,  the  difference  in  position,  I  contend  that  the  differences  in 
position  were  only  those  which  a  waterspout  drawing  itself  up  into  its 
cloud,  and  then  coming  down  again,  must  necessarily  take  in  conse- 
quence of  tho  constant  southeastward  progress  of  the  storm.  It  could 
not  come  down  in  the  same  place  any  more  than  a  circus  rider  can  when 
he  leaps  up  from  the  back  of  a  running  horse  und  comes  down  again 
several  feet  ahead  of  his  former  position.  The  successive  phases  of 
this  waterspout,  In  their  positions,  follow  strictly  the  eastward  move- 
ment of  the  tornado  cloud,  and  inspection  of  the  three  photographs  of 
Chamberlain's  sot  shows  that  a  lino  between  the  first  and  last  phase  of 
his  three  would  pass  through  the  position  of  the  intervening  one. 

This  may  seem  a  matter  of  little  consequence  in  terminology;  but  it 
is  of  importance  in  view  of  the  fact  that  the  expressions  "two  water- 
spouts", "several  waterspouts",  etc.,  are  positively  needed  for  cases 
where  two  or  more  entirely  independent  phenomena  of  the  kind  are  in 
sight  at  the  same  time,  or  nearly  so;  as  when  a  friend  of  mine  once  saw 
eleven  waterspouts  on  the  ocean  simultaneously. 

I  will  now  give  a  brief  description  of  the  successive  phases  of  the 
waterspout  as  I  observed  it. 

I  was  standing  on  my  own  private  boat  wharf,  which  is  on  the  sea- 
shore at  the  extreme  southeast  point  of  Cottage  City,  one-half  mile  ex- 
actly south  of  tho  "Oak  Bluffs"  or  main  wharf,  the  wharf  shown  in 
Coolidge's  photograph,  No.  7933,  fig.  28,  a  little  after  half-past  twelve. 
In  the  excitement  of  the  occurrence  I  failed  to  note  the  exact  time  An 
exclamation  from  a  friend  standing  near  mo  drew  my  attention  to  the 
waterspout,  which  had  just  formed  in  the  rear  of  a  black  thundersquall 
which  we  had  been  watching  to  the  southeast,  the  wind  being  from  the 
northwest.  The  waterspout  being  a  mile  or  more  in  the  rear  of  the  squall 
and  separated  from  it  by  a  clear  interval,  was  a  little  north  of  oast  from 
my  position  of  observation;  it  appeared  to  be  somewhat  nearer  than  the 
Sueconesset  light-ship  (on  Succonesset  Shoals),  which  is  nine  (9)  miles 
easterly  from  Cottage  City;  at  the  same  time  it  was  evidently  nearly  as 
far.  I  had  several  interviews  subsequently  with  captains  of  the  local 
fishing  catboats,  all  men  of  lifelong  experience  as  coasters,  with  refer- 
ence to  the  probable  distance  of  the  spout.  They  all  estimated  It  as 
from  eight  to  ten  miles  away;  no  one  gave  a  less  estimate  than  eight 
miles.  All  but  one  of  the  captains  had  seen  it  only  from  Cottage  City. 
One  captain,  however,  told  me  that  he  was  sailing  to  Cottage  City  from 
Cape  Poge,  a  point  seven  miles  to  the  southeast  of  Cottage  City,  and 
saw  the  waterspout  when  he  was  off  that  cape,  and  that  it  was  certainly 
nearer  to  Cottage  City  than  the  Succonesset  light-ship  (which  from  his 
position  would  be  much  in  the  same  direction);  ho  said  it  was,  in  his 
judgment,  about  one  mile  nearer  to  Cottage  City  than  the  light-ship; 
this  is  excellent  testimony  on  this  point,  and  I  think  wo  may  safely  set 
the  distance  of  the  waterspout  from  the  Cottage  City  wharf  as  having 
been  just  about  eight  miles. 

At  this  first  phase  the  waterspout  was  very  tall  and  very  thin;  in  fact 
it  presented  very  much  the  same  appearance  as  in  No.  3  of  Chamberlain's 
set,  fig.  35,  though  in  a  much  more  northwesterly  position;  at  its  base 
was  a  spherical  mound  of  up-whirling  water  and  spray  several  times 
wider  than  the  main  portion  of  the  column,  a  white  dot  of  foaming  water 
appearing  at  tho  center  of  this  mound  at  the  ocean's  surface;  the  column 
was  sinuous  and  moderately  expanded  as  it  joined  the  cloud.  The  tor- 
nado cloud  had  a  broad,  flat,  angry  looking  under  surface,  little  tufts  of 
mist  or  rain  descending  from  it  here  and  there;  it  extended  at  least  a 
mile  to  tho  oast  and  southeast,  joining  the  thundersquall  in  the  latter 
course.  Toward  the  north  and  west  it  was  much  less  extensive,  and 
in  fact  more  than  one-half  of  the  sky  over  Cottage  City  was  in  bright 
sunlight.  At  times  it  appeared  as  if  streaks  of  rain  were  descending 
from  the  tornado  cloud  to  the  ocean  all  around  the  waterspout  in  all  its 
successive  phases. 

This  first  phase  is  not  xhown  in  any  of  the  professional  photographs, 
though  probably  some  amateur's  camera  may  have  caught  It.  Compara- 
tively few  persons  saw  it,  that  is  only  those  who  happened  to  be  at  the 
beach;  the  morning  bathing  hour  was  mostly  over;  the  professional  pho- 
tographers were  In  their  offices  inland;  it  took  time  to  get  word  to  them 
and  for  them  to  bring  out  their  instruments  and  get  them  placed  in  good 
positions.  Meanwhile,  this  first  phase  faded  away,  and  that  one  of  tho 
views  of  the  photographers  which  is  generally  called  the  "first  water- 
spout "  is  not  at  all  the  first,  but  the  second  phase,  and  a  much  larger 
and  grander  one.  The  second  phase,  which  appeared  at  about  a  quarter 
to  one  o'clock,  was  by  far  the  grandest  one  of  all.  It  is  the  "  first"  one 
of  the  photographers,  the  one  shown  by  Mr.  Coolidge's  photograph 
numbered  7933,  fig.  28.  It  began  by  the  formation  of  a  broad  funnel  on 
the  under  side  of  the  tornado  cloud,  which  then  became  a  very  broad 
black  tube.  This  rapidly  stretched  down  to  the  ocean,  where  it  raised 
a  large  mound  of  whirling,  foaming,  rising  water  at  the  center,  and  of 


spray  around  its  margin.  The  white  center  of  upward  rushing  water 
was  usually  clearly  visible  to  the  naked  eye,  and  through  a  Bold  glass 
was  very  marked.  At  other  times  it  was  completely  obscured  by  the 
surrounding  mist  and  spray,  and  was  never  relatively  large  to  tho  view, 
because  so  thoroughly  enveloped.  *  *  *  There  was  no  white  water 
vi.-iblo  at  any  time  in  the  tube  proper,  above  the  mound.  This  phase 
lasted  probably  about  fifteen  minutes,  during  which  it  varied  in  form 
from  a  slender,  even  cylinder,  to  a  massive,  imposing  conical  tube,  a^  it 
swept  on  slowly  and  majestically  to  the  southeast. 

From  this  phase  we  are  enabled,  through  Mr.  Chamberlain's  valuable 
set  of  photographs,  to  trace  the  forward  progress  of  tho  tornado  cloud 
visibly,  and  the  relations  of  this  and  tho  succeeding  phase  to  each  other, 
since  these  three  views  were  taken  by  the  same  camera  and  lens,  and 
from  exactly  the  same  point.  (I  have  established  this  point,  as  it  is 
easy  for  any  one  to  do,  on  the  spot,  by  taking  a  position  on  the  west  mar- 
gin of  the  main  portion  of  the  Ocean  Park  adjoining  the  Oak  Bluffs  dock, 
where  the  relative  positions  of  the  telegraph  poles,  and  their  several 
arms  and  wires  can  be  made  to  coincide  exactly  with  their  relative  posi- 
tions in  tho  photographs.  It  will  bo  noted  that  these  positions  arc  ex- 
actly the  same  in  the  three  views,  though  in  the  last  one  the  camera  was 
revolved  more  to  the  southeast  than  in  tho  others.  This  point  of  obser- 
vation proves  to  have  been  at  the  center  of  the  convex  western  edge  of 
the  main  body  of  the  park,  just  cast  of  the  carriage  road  which  extends 
in  a  curve  from  one  point  of  the  Sea  View  avenue  to  another  point  of 
the  same  avenue  around  the  west  edge  of  this  main  portion  of  the  park. 
It  is  called  Ocean  avenue.  The  point  whore  the  camera  stood  is  just 
east  of  Ocean  avenue,  where  a  straight  lino  running  through  the  east 
end  of  Fisk  avenue  would  strike  it.) 

Now,  in  examining  Chamberlain's  first  view,  fig.  27,  where  the  grandest 
phase  is  seen,  the  waterspout  is  shown  a  little  north  of  the  two  central 
telegraph  posts  of  the  view,  while  a  schooner  is  seen  sailing  southeast 
about  three  or  four  miles  from  the  shore,  some  little  distance  to  tho 
north  of  the  waterspout.  Also,  a  little  northerly  of  the  waterspout, 
about  a  third  of  the  apparent  distance  (in  the  view)  between  it  and  the 
schooner,  the  masts  of  a  vessel  at  anchor  appear  ou  the  horizon.  This 
is  apparently  the  Succonesset  light-ship,  nine  miles  away.  It  is  cer- 
tainly about  the  position  of  that  light-ship,  and  resembles  closely  its 
familiar  appearance,  as  seen  from  Cottage  City.  This  would  seem  to 
locate  exactly  the  direction  of  this  phase  of  tho  phenomenon  from  Cot- 
tage City.  As  my  charts  of  Nantucket  Sound  (or  Vineyard  Sound)  are  at 
Cottage  City,  and  my  notes  made  on  the  spot  are  lost,  I  can  not  at  this 
time  state  the  bearing  of  the  light-ship  from  tho  point  mentioned  as  tho 
position  of  Chamberlain's  camera;  but  it  can  easily  be  settled  by  reference 
to  such  a  chart. 

Mr.  Coolidge's  photograph  No.  7934,  fig.  32,  seems  to  show  a  later 
form  of  this  phase,  the  column  having  grown  thicker  and  more  evenly 
conical  since  Chamberlain's  first  and  earlier  view  was  taken.  This  ap- 
pears from  the  fact  that  the  schooner  is  now  much  nearer  to  the  line  of 
direction  of  the  waterspout,  in  which  direction  she  was  sailing  faster, 
apparently,  than  the  spout  was  moving  in  the  same  direction.  It  is  true 
that  Coolidge's  standpoint  was  evidently  to  the  north  of  Chamberlain's, 
being  near  the  steamboat  dock,  and  quite  near  the  shore,  while  Cham- 
berlain's position  was  about  five  hundred  feet  from  the  shore.  But  when 
all  allowances  for  difference  in  position  have  been  made,  there  seems  to 
be  still  quite  a  margin  which  eau  only  be  explained  by  the  fact  that  the 
vessel  had  actually  had  time  to  sail  some  distance  southeasterly. 

When  this  grandest  phase  disappeared  the  spout  was  for  a  few  minutes 
totally  absorbed  into  the  cloud.  Then,  while  I  was  closely  watching  it 
for  further  developments,  a  whirling  funnel  began  to  bulge  down  from 
the  tornado  cloud,  while  at  the  same  moment,  and  before  the  funnel  was 
more  than  a  mere  projecting  knob  on  the  cloud,  the  water  on  the  surface 
of  the  sound  just  beneath  began  to  boil  furiously,  and  to  rise  up  in  a 
whirling  mound,  indicating  a  line  of  vortex  motion  already  established 
the  entire  distance  between  the  cloud  and  the  sea.  Next,  while  the 
upper  tube  began  to  extend  downward,  a  central  portion  of  the  tube  was 
formed,  entirely  independent  of  the  upper  and  lower  portions,  as  clear 
spaces  existed  between. 

This  Is  finely  shown  in  Chamberlain's  second  photograph,  fig.  34,  where 
the  three  portions  are  distinctly  seen  before  their  union.  Many  per- 
sons on  seeing  his  three  views  take  tho  one  which  shows  the  waterspout  as 
a  very  slim  tortuous  tube,  fig.  35,  as  the  first  exhibition  of  a  waterspout, 
of  which  the  one  in  three  portions  is  but  the  breaking  up  phase.  That 
this  is  not  the  case  is  indicated  by  my  own  most  positive  observation  of 
the  triple  formation  of  the  spout,  to  which  I  called  tho  attention  of  by- 
standers at  the  time.  But,  further,  the  photographs  themselves  prove 
the  incorrectness  of  that  idea;  for  it  will  be  noted  that  in  the  view  of 
the  spout  having  the  triple  structure,  fig.  34,  the  column  has  just  passed 
from  its  second  phase,  where  it  appeared  a  little  to  tho  north  of  the  pair 
of  central  telegraph  posts,  to  a  position  a  little  to  the  south  of  the  more 
northerly  of  these  posts,  while  the  schooner  has  passed  to  a  central 
position  between  them.  In  the  other  view,  fig.  35,  the  column  has  come 
near  to  the  more  southerly  of  the  posts,  while  the  schooner  has  passed 
considerably  to  the  south  of  both,  and  lias  been  closely  approached  by 
a  tug  towing  three  barges,  which  was  only  just  coming  into  view  in  the 
other  photograph. 

I  need  only  to  remark  further,  therefore,  in  this  connection,  that  the 


JULY,  1906. 


MONTHLY  WEATHER  REVIEW. 


311 


third  of  Chamberlain's  set  of  photographs,  fig.  35,  represents  the  com- 
pleted form  of  the  waterspout  shown  in  the  second  view,  and  the  third 
and  last  actual  phase  of  the  entire  phenomenon.  As  this  phase  dis- 
appeared at  about  1 :25  p.  m.,  the  entire  occurrence  covered  a  little  over 
three-quarters  of  an  hour. 

If  one  were  disposed  to  form  some  estimate  of  the  rate  of  progress  of 
the  waterspout,  from  that  of  the  schooner,  the  following  points  would 
deserve  consideration : 

1.  Though  the  wind  was  violent  in  the  vicinity  of  the  squall,  there  was 
but  a  moderate  wind  on  the  shore  and  in  the  vicinity  of  the  schooner. 
This  is  not  a  matter  of  my  recollection  alone,  for  the  photographs  show 
it;  the  sea  near  the  shore  is  little  disturbed,  while  the  schooner  carries  all 
sail  except  topsails,  and  has  no  reefs.     If  we  may  estimate  the  probable 
length  of  her  hull  as  75  feet  (a  moderate  estimate),  she  must  have  gone 
somewhat   over   half   a   mile  during  three-quarters   of  an   hour.     Her 
course  being  somewhat  oblique  to  the  line  of  vision,  and  veering  away 
from  the  observer,  is  really  longer  than  it  measures  on  the  photograph. 
The  tide  runs  with  great  force,  and  may  have  worked  against  the  schooner. 

2.  The  waterspout  was  certainly  twice  as  far  away  as  the  schooner. 
Supposing,  as  is  very  likely  from  evidence  elsewhere  offered,  that  it  was 
just  about  twice  as  far,  and  moving,  as  appears  to  have  been  the  case-, 
in  the  same  course,  the  tornado  cloud  and  the  waterspout  must  have 
progressed  considerably  less  than  twice  as  fast  as  the  schooner,  since  the 
latter,  starting  from  a  spot  considerably  to  the  north  of  the  spout  passed 
to  the  south  of  it. 

Toward  the  close  of  this  phenomenon  the  eastern  half  of  the  sky  be- 
came quite  black  with  clouds,  while  the  entire  western  half,  where  the 
Cottage  City  observers  were,  was  brilliant  with  sunlight,  which  at  this 
hour  glanced  easterly  beneath  the  blackness.  The  chromatic  effects 
were  of  an  indescribably  rare  and  beautiful  kind.  The  surface  of  the 
sound  for  several  miles  out  was  lighted  up  with  weird  hues  of  bright 
blue,  green,  yellow,  and  gray,  in  patches,  according  to  the  nature  of  the 
variable  weedy  and  sandy  bottom,  greatly  Intensified  by  the  solemn, 
black  storm  clouds  and  waterspout  overhead.  Thousands  of  spectators, 
crowding  the  beach,  gazed  on  the  sight  with  mingled  admiration  and  awe. 

I  append  some  estimates  of  the  probable  dimensions  of  the  waterspout 
founded  on  its  apparent  distance,  as  ascertained  by  investigation,  and 
upon  measurements  of  the  photographs,  using  as  a  unit  the  hull  of  the 
schooner  in  view,  estimated  as  75  feet  long  and  four  miles  from  shore. 
I  am  inclined  to  think  that  the  schooner's  distance  was  nearer  three 
than  four  miles,  and  that  the  estimates  should  be  increased  proportion- 
ally. By  my  estimate  the  waterspout  would  have  an  altitude  of  about 
half  a  mile. 

The  conditions  of  the  photographs  of  Chamberlain's  series  might  afford 
another  basis  for  an  estimate. 

By  ascertaining  the  distance  from  the  spot  where  the  camera  stood  to 
the  higher  one  of  the  central  pair  of  telegraph  posts  (as  the  other  stands 
on  lower  ground),  which  distance  is  not  far  from  500  feet,  and  the  height 
of  the  telegraph  post,  and  assuming  the  probable  distance  of  the  water- 
spout as  eight  miles,  triangles  could  be  constructed  from  which  the 
height  might  be  calculated,  provided  that  the  telegraph  posts  were  not 
so  near  to  the  camera  as  to  be  disproportionately  magnified.  I  suppose 
corrections  might  be  applied  for  such  irregularity  if  the  power  of  the 
lens  were  known. 

Rough  estimates  as  to  dimensions  of  the  icaterspoui  seen  from  Cottciije  City, 
Mass.,  Augitst  I'.i,  1896. 

(1)  Estimates  founded  on  photograph  No.   7934,    fig.  32,  taken  by 
Coolidge,  and  based  on  the  supposition  that  the  waterspout  was  eight 
miles  from  Cottage  City,  and  that  the  schooner  visible  to  the  north  of  it 
is  75  feet  long  and  four  miles  from  Cottage  City.     In  this  photograph, 
the  schooner's  hull  (not  including  the  bowsprit),  estimated  at  75  feet, 
measures  one-tenth  inch.     The  waterspout  being  twice  as  far  distant 
should  therefore  measure  150  feet  for  every  one-tenth  inch  of  dimension. 
Some  correction  should  be  made,  in  strict  calculation,  for  the  tendency  of 
the  camera  to  magnify  near  objects  more  than  distant  ones;  but  this  is 
comparatively  slight  for  two  objects  both  of  which  are  distant,  and  may 
be  disregarded  in  a  rough  estimate. 

Using  this  unit  of  measurement,  1-10  inch  on  the  photograph  corres- 
ponds to  75  feet  at  the  schooner,  or  150  feet  at  the  spout: 

Feet. 
Height  from  surface  of  ocean  to  lower  edge  of  cloud 

(=  1.917  inches) 2874 

Mound  of  spray  at  base  of  the  spout: 

Height 600 

Breadth 750 

Breadth  of  the  mass  of  foaming  water  in  this  mound  .     150 
Tube  or  funnel  proper,  above  the  base  mound: 

Breadth  (diameter)  just  above  the  mound 150 

Breadth  about  the  middle 300 

Breadth  at  extreme  top  where  it  joins  the  cloud . . .     600 

(2)  Estimates  founded  on  a  photograph  by  Chamberlain,  fig.  27,  and 
called  by  him  the  "  first  "  waterspout.     It  shows  the  spout  of  larger  size 
and  grander  appearance  than  the  later  views.     These   estimates  are 
based  on  the  assumed  length  of  the  schooner  in  sight,  and  its  distance, 
assisted  by  known  facts  as  to  the  position  of  the  ship  channel,  and  on 


the  supposed  distance  of  the  waterspout,  judging  from  reports  of  cap- 
tains of  fishing  boats  who  got  its  range.  This  is  really  the  second  and 
not  the  first  stage  or  appearance  of  the  spout,  as  witnessed  by  myself 
from  its  very  beginning. 

In  this  photograph  the  hull  of  the  schooner  (75  feet)  measures  13-100 
of  an  inch.  Its  estimated  and  probable  distance  is  not  over  four  miles, 
that  of  the  waterspout  eight  miles.  Hence  the  unit  of  measurement, 
13- 100  inch,  would  cover  150  feet  at  the  waterspout.  The  dimensions 
would  then  be  as  follows: 

Feet. 

Height  from  ocean  to  cloud 2600 

Height  of  basal  mound  of  spray 300 

Width  (diameter)  of  basal  mound  of  spray 600 

Tube  proper: 

Width  at  lowest  point 150 

Width  at  middle  point 100 

Width  at  top 375 

Remarks.— This  photograph  represents,  as  I  can  testify  from  personal 
observation,  the  same  spout,  or  phase  of  the  spout,  as  Coolidge's  No. 
7934;  but  at  a  different  minute  of  its  existence,  since  the  form  is  consid- 
erably different.  The  spout  was  changing  constantly  in  length  and 
width  within  certain  limits,  but  was  throughout  the  largest  of  the  phases. 
The  difference  in  the  apparent  length  of  the  schooner's  hull  from  that  in 
Coolidge's  photograph  is  due  probably  to  a  stronger  lens. 


(G)  LETTER  OF  E.  U.  HANKS,  TO  THK  EDITOR.    DATKD  COTTAGK  CITY,  MASS., 
OCTOUKR  26,  1896. 

Your  letter  of  October  20  is  at  hand.  I  am  sorry  to  say  that  I  do  not 
know  of  any  scientific  observations  of  the  waterspout  seen  in  Vineyard 
Sound,  August  19.  I  had  an  excellent  view  of  it  throughout  its  entire 
duration,  a  portion  of  the  time  through  a  six-inch  astronomical  telescope. 
It  occurred  August  19, 1896,  at  about  1  o'clock  p.  m.  It  had  been  a  calm 
summer  day,  with  but  few  clouds,  temperature  about  70°,  with  but  little 
variation  before  and  after  the  phenomenon.  It  has  been  stated  that 
there  were  two  or  three  waterspouts ;  this,  I  think,  is  hardly  correct,  as 
no  one  saw  more  than  one  at  the  same  time,  the  so-called  different  ones 
being  different  forms  or  reformations  of  the  same  spout.  Its  beginning  was, 
from  my  point  of  view  at  Cottage  City,  about  six  miles  distant,  in  a  line 
toward  Cotuit;  its  ending,  about  eight  miles,  in  a  line  toward  Hyannis. 
It  had  a  steady  progressive  movement  and  was  inclined  forward  in  the 
direction  of  advance.  I  estimate  its  forward  movement  at  about  eight 
miles  in  the  thirty-five  minutes  it  continued.  During  the  time  of  the 
waterspout,  showers,  with  lightning,  could  be  seen  preceding  and  follow- 
ing it  in  its  course;  about  an  hour  afterward  Cottage  City  was  visited  by  a 
tempestuous  downpour  of  rain.  Through  my  telescope  the  column 
seemed  to  be  surrounded  by  a  dense  vapor,  which  radiated  like  smoke 
from  its  edges,  and,  condensing,  fell  in  torrents  of  rain  for  a  distance  in 
either  direction  about  equal  to  the  diameter  of  the  column.  At  first  the 
edges  of  the  column  were  quite  well  defined,  later  it  grew  much  larger 
in  diameter  and  more  diffuse,  its  height  remaining  the  same  throughout. 
While  I  could  not  penetrate  with  my  telescope  the  enveloping  mist  so  as 
to  see  if  there  was  a  solid  or  tubular  mass  of  water  either  ascending  or 
descending  the  inner  part  of  the  spout,  nor  detect  a  whirling  or  spiral 
movement,  yet  the  funnel  shape  at  the  top  and  general  appearance  indi- 
cated that  character.  Based  upon  estimates  of  the  most  careful  obser- 
vers, its  probable  size  was  from  KlO  to  300  feet  in  diameter  at  different 
periods,  and  4000  to  5000  feet  high.  Where  the  column  joined  the  sea 
there  was  a  great  churning  and  splashing  of  the  water,  which  extended 
as  white  mist  for  200,  or  more,  feet  upward  and  outward;  this  was  more 
pronounced  toward  the  last.  When  the  spout  finally  disappeared  it  grew 
slender  and  broke  about  midway  of  its  height,  the  lower  portion  drop- 
ping into  the  sea  and  the  upper  dissipating  into  the  cloud. 


(II)  EXTRACT  FROM  THE  REPORT  OF  THE  CLIMATE  AND  CROP  SERVICE,  NKW  ENKLASD 
SECTION,  AUGUST,  1896,  BY  J.  WARREN  SMITH,  SECTION  DIRECTOR. 

On  August  19  three  well-defined  and  magnificent  waterspouts  were 
observed  in  Vineyard  Sound,  between  the  eastern  edge  of  Marthas  Vine- 
yard and  the  mainland,  about  off  Succonesset  Shoal. 

Mr.  W.  W.  Neifert,  the  Weather  Bureau  observer  at  Vineyard  Haven, 
writes :  "  During  the  entire  forenoon  the  weather  was  partly  cloudy  and 
sultry,  with  great  masses  of  cumulus  clouds  in  the  north  and  northeast ". 
|  The  remainder  of  this  quotation  is  practically  identical  with  (A)  above. — 
EDITOR.] 

We  have  reports  of  the  phenomenon  from  Mr.  E.  H.  Garrett,  Vho  ob- 
served it  from  the  coast  between  Hyannis  and  Oysterville;  from  John 
B.  Garrett,  who  saw  it  from  Falmouth  Heights,  and  from  Dr.  S.  W.  Ab- 
bott, Secretary  of  the  State  Board  of  Health,  who  was  in  West  Falmouth 
Harbor  at  the  time. 

Mr.  E.  H.  Garrett  says:  "We  were  out  on  the  beach  and  saw  an  odd  look- 
ing cloud  in  the  sky.  It  seemed  to  have  a  curious  appendage  at  first, 
which  one  of  the  party  described  as  looking  like  '  an  icicle.'  We  turned 
to  go  home,  when  one  of  the  group  looking  back  saw  the  '  icicle '  chang- 
ing, and  we  all  watched.  It  grew  larger,  then  looked  like  a  long,  thin, 
gray  veil  of  mist  and  as  it  descended  the  water  from  the  Sound  began  to 
rise.  I  watched  it  carefully  and  should  say  It  was  over  300  and  nearer 
500  feet  high,  and  in  comparison  with  the  measurement  of  schooners 


MONTHLY  WEATHER  REVIEW. 


JULY,  1906 


lying  near  it,  it  certainly  could  not  have  been  less  than  125  feet  in  di- 
ameter". 

Mr.  John  B.  Garrett  saw  it  from  Falmouth  Heights  in  an  east-south- 
east direction,  and  its  distance  was  estimated  to  be  from  six  to  ten 
miles.  He  says:  "In  form  it  was  much  like  a  short  section  of  rubber 
pipe,  flexible,  and  of  the  color  of  a  heavy  watery  cloud.  It  was  tele- 
scopic, the  upper  end  of  the  column  vanishing  in  the  small  end  of  a  fun- 
nel-shaped cloud  somewhat  larger  than  itself. 

"  Shortly  before  it  broke  and  disappeared,  the  main  column  drew  up- 
ward, disclosing  at  its  lower  end  a  smaller  column  or  tube  within  the 
main  one.  There  was  also  visible  for  a  time,  as  it  broke,  a  distiuct 
spiral  and  rotary  motion,  extending  about  one-third  the  length  of  the 
column  from  its  upper  end. 

"  During  the  whole  appearance  the  water  at  its  base,  considerably 
wider  than  the  column,  was  churned  into  a  seething  mass  and  raised  to  a 
great  height. 

"  If  the  estimate  of  the  distance  from  Falmouth  Heights  be  approxi- 
mately correct,  your  previous  correspondent'^  estimate  of  the  diameter 
of  the  waterspout,  125  feet,  must  be  within  rather  than  beyond  the 
actual;  and,  assuming  this  as  correct,  the  height  of  the  column  can  not 
have  been  less  than  750  feet.  The  height  to  which  the  spray  was  thrown 
was  decidedly  greater  than  the  width  of  the  column,  and  must,  there- 
fore, be  estimated  above  125  feet  ". 

Doctor  Abbott  estimates  the  height  of  the  waterspout  to  have  been 
3000  or  4000  feet,  judging  from  its  appearance  above  a  distant  hill,  and 
the  "  probable  distance  away  of  the  phenomenon  ".  He  says:  "  From  all 
that  I  can  learn,  the  waterspout  was  about  25  miles  distant".  But  it 
could  not  have  been  that  distance  away  from  him,  and  yet  have  been 
seen  in  an  "  east-southeast  "  direction  from  Falmouth  Heights,  and  in  a 
"northerly"  direction  from  Vineyard  Haven.  Still  from  his  point  of 
view,  at  ten  miles  distance,  it  must  have  been  over  10UO  feet  in  height. 
He  writes  that  "  the  waterspout  was  soon  followed  by  marked  atmos- 
pheric disturbances.  Thunder,  lightning,  hail,  and  rain  in  abundance 
fell  within  an  hour  or  more.  A  dense,  dark  cloud  formed  in  the  north- 
west, followed  by  a  squall  from  the  southwest,  and  the  wind  shifted  in 
a  short  time  from  northeast  to  southeast,  and  then  by  southwest  to 
northwest.  The  thermometer  at  2:0u  p.  m.  indicated  56°,  a  very  low 
reading  for  a  place  where  it  has  varied  but  little  from  70°  all  summer  ". 


(I)  COPY  OF  LETTER  OF  REV.  CRANDALI.  J.  NORTH,  OF  NEW  HAVEN,  CONN.,  IN  THE 
CHRISTIAN  ADVOCATE  FOB  SEPTEMBER  24,  1896. 

Thousands  of  summer  residents  of  Marthas  Vineyard,  Nantucket,  and 
the  adjacent  Massachusetts  coast  were  treated  to  a  spectacle  of  remark- 
able grandeur  one  day  in  August,  last.  Guests  at  the  hotels  and  occu- 
pants of  cottages  at  the  various  resorts  were  just  rising  from  dinner 
when  the  cry  was  raised,  "A  waterspout,  a  waterspout !"  The  scene 
presented  to  view  was  such  as  not  one  in  a  thousand  had  ever  wit- 
nessed before  or  would  ever  see  again. 

A  large  mass  of  heavy  black  cloud  hung  high  above  the  ocean  between 
Nantucket  and  Cape  Cod.  Suddenly  it  was  seen  to  project  a  circular 
column  of  its  own  dense  vapor  perpendicularly  downward,  rapidly  but 
not  precipitantly,  until  sea  and  cloud  were  connected  by  a  cylinder  one 
or  two  hundred  feet  in  diameter,  straight  as  a  pine  tree,  and  at  least  a 
mile  high.  It  was  a  waterspout  indeed,  of  most  unusual  proportions 
and  indescribable  beauty. 

The  sea  was  perfectly  calm,  the  air  almost  motionless,  the  sun  shining 
brightly,  light  summer  clouds  hangiug  here  and  there  over  the  deep  blue 
sky;  and  in  strange  contrast  with  all  the  rest,  was  this  lofty  ihass  of 
black  vapor  with  its  absolutely  perpendicular  support.  To  add  to  the 
weird  effect  occasional  livid  streaks  of  forked  lightning  shot  athwart  the 
black  monster  cloud  above.  The  column  was  only  slightly  funnel-shaped 
just  where  it  joined  the  cloud,  and  was  of  equal  diameter  the  remainder 
of  its  length.  At  its  ba*e  th«  sea  was  lashed  into  a  mass  of  white  foam 
and  spray  that  mounted  upward  as  high  as  the  masts  of  a  large  schooner. 

From  Cottage  City  it  seemed  about  six  miles  distant,  but  careful  obser- 
vation through  a  glass  from  the  writer's  view-point  showed  that  it  was 
nearly  in  line  with  the  light-ship  off  Hyannis  Harbor,  and  still  farther 
distant,  its  foot  resting  upon  the  sea  beyond  the  horizon  line.  It  must 
have  been  twenty  or  twenty-five  miles  away,  but  such  was  its  magnitude 
that  it  seemed  not  more  than  one  quarter  of  that  distance. 

It  moved  slowly  eastward,  and  continued  with  little  change  in  form 
for  seventeen  minutes.  Then  it  gradually  attenuated  till  it  looked  like 
a  dark  nbbon  hanging  out  of  the  cloud,  and  at  length  disappeared.  The 
lashing  of  the  water  into  foam  and  spray  where  its  base  had  rested  con- 
tinued unabated,  which  was  evidence  that  the  waterspout  was  still  there, 
though  now  invisible,  and  that  it  might  be  expected  to  reappear.  Surely 
enough,  after  an  interval  of  about  ten  minutes,  the  cylindrical  form  of 
black  vapor  began  to  push  its  way  downward  again  from  the  cloud  and 
continued  until  it  stood  again  upon  the  white  mass  of  foam  and  spray 
mounting  up  from  the  sea  surface.  This  time  its  top  was  more  funnel- 
shaped  and  curved  to  the  eastward.  It  continued  eight  minutes  and 
disappeared.  The  projecting  of  the  visible  vapor  downward  caused  the 
illusion  that  its  origin  was  from  the  cloud  rather  than  from  the  sea,  and 
many  supposed  that  it  was  a  cloud-burst  rather  than  a  waterspout;  but 
this  is  disproved  by  the  continuance  of  the  agitation  of  the  sea  surface 


during  the  interval  between  the  disappearance  of  the  first  column  of 
visible  vapor  and  the  formation  of  the  second.  Also  the  descent  of  the 
column  was  too  slow  for  a  mass  of  water  falling  from  a  cloud-burst,  as 
was  clearly  apparent  a  little  later,  when  a  real  cloud-burst  occurred  upon 
the  mainland  opposite,  in  full  view  from  our  point  of  observation. 

The  apparent  formation  from  top  downward  was  due  to  the  fact  that 
the  atmosphere  became  more  rarefied  by  the  swifter  gyrations  of  the 
whirlwind  at  the  higher  altitude,  causing  the  invisible  vapor  carried  up 
from  the  sea  surface  to  condense  and  become  visible  at  the  highest  level 
first;  then  its  visibility  gradually  extended  downward  as  the  velocity  of 
the  gyrations  below  increased.  The  whirlwind  lashed  the  sea  into  foam 
and  spray  and  vapor,  and  stood  it  up  in  an  invisible  column ;  but  it 
turned  into  cloud  at  the  top  first,  then  downward  its  entire  length,  until 
there  it  stood  for  many  minutes  before  the  wondering  gaze  of  thousands, 
a  veritable  "  pillar  of  cloud  by  day". 

The  old  sea  captains  of  Marthas  Vineyard  said  that  this  waterspout 
exceeded  in  size  and  grandeur  anything  of  the  kind  they  had  seen  dur- 
ing all  of  their  seafaring  experience.  Enterprising  photographers  se- 
cured several  good  photographs  of  the  remarkable  phenomenon. 


(J)  COPY  OF  DESCRIPTION  BY  DR.  F.  C.  V.  II.  VOM  SAAL;  APPARENTLY  COMPILED 
FROM  OBSERVATIONS  AT  COTTAUE  ClTY,  AND  PUBLISHED  IN  TUE  SCIENTIFIC  AMERI- 
CAN, NEW  YORK,  SSEPTEMIIER  26, 1896. 

About  12:30  p.  m.,  August  19,  1896,  one  of  the  very  dark  clouds  hover- 
ing over  Vineyard  Sound,  between  the  mainland  and  Cottage  City,  was 
seen  to  send  out  a  downward  and  sharply  pointed  streak  of  cloud  matter, 
whose  funnel-shaped  basis  above  was  not  at  all  times  visible.  After  a 
duration  of  about  fifteen  minutes  it  broke  and  completely  vanished  The 
apparition  quickly  emptied  of  their  summer  residents  all  the  cottages 
along  the  bound  and  adjacent  islands,  Nantucket  included.  No  photo- 
graphs were  taken  of  this  "first  spout,  to  my  knowledge. 

Shortly  afterward  a  long  tongue  emanated  from  the  same  clouds,  and 
was  slowly  pushed  downward  to  a  point  about  100  feet  from  the  surface 
of  the  ocean.  Its  height  was  certainly  a  mile,  and  the  band-like  shape 
gradually  increased  in  width.  With  a  glass,  slow  gyratory  movements 
could  be  detected,  also  longitudinal  stripes  caused  by  falling  water. 
This  cloud-burst4  made  the  water  below,  over  a  surface  of  many  hundred 
yards,  look  like  a  boiling  pool.  The  jumping  spray  from  this  was  also 
caught  and  drawn  upward  into  the  whirl  toward  the  downpouring  col- 
umn. This  latter,  now  of  lighter  color,  being  struck  by  the  sun,  was 
gradually  withdrawn  upward,  evidently  thinning  and  broadening  toward 
its  base.  With  a  glass,  mists  could  still  be  seen  falling  into  the  snow- 
white  foaming  area  below.  The  duration  of  this  second  and  most  perfect 
phenomenon  of  i  he  day  -  there  were  three  in  all— was  about  half  an  hour. 

About  twenty  minutes  after  its  disappearance  a  third  began  to  form, 
gradually  coming  downward  from  the  same  clouds,  though  from  a  spot 
a  little  farther  north;  but  it  hardly  reached  completion.  It  is  very  im- 
portant to  note  that,  in  this  third  case,  the  ocean  below  was  entirely 
quiet  for  a  time,  being  only  disturbed  later  on,  when  the  same  process 
of  condensation,  mentioned  above,  caused  a  similar  downpouring,  espe- 
cially noticeable  in  the  period  of  retraction.  It  was  soon  apparent  that 
the  agency  causing  the  spouts  had  spent  its  energy;  the  column  was 
eUdently  thinner  in  substance  and  its  formation  slower  and  hesitating. 
It  stopped  midway,  sending  only  an  attenuated  end  farther,  to  be  with- 
drawn upward  soon  after. 

During  almost  all  of  the  time  since  the  appearance  of  the  first  spout 
there  was  a  heavy  rainstorm  accompanied  by  flashes  of  lightning  from 
the  northern  and  darkest  portion  of  the  long  motionless  stratum  of 
clouds  above  mentioned. 

Cottage  City,  which  had  been  in  sunshine  until  then,  was  visited  by  a 
drenching  rain  some  hours  later. 

The  long  duration  of  the  phenomena  just  described  enabled  the 
writer  to  form  a  somewhat  different  opinion  of  the  nature  of  such  water- 
spouts from  what  is  commonly  held.  True,  I  must  fall  back  upon  the  old 
(or  rather  older)  explanation,  that  such  whirls  are  caused  by  two  winds 
striking  each  otherat  an  obtuse  angle.  The  greatest  rotary  velocity  must 
be  placed  at  the  spot,  about  100  feet  above  the  ocean,  toward  which  the 
cloud  matter  from  above  and  the  spray  from  below  were  drawn.  As 
condensation  was  continually  transforming  this  cloud  matter  into  water, 
it  stands  to  reason  that  by  far  greater  quantities  of  it  were  drawn  down 
than  was  apparent  to  the  eye. 

But  the  spout  is  from  above  and  not  from  below,  as  a  glance  at-  the  cut 
conclusively  proves.  This  also  definitely  settles  the  question  as  to  what 
part  the  ocean  takes  in  the  constitution  of  the  column,  which  is  prac- 
tically none.  The  "boiling  as  if  in  a  caldron"  is  not  caused  by  the 
action  of  the  circling  wind,  but  by  the  great  quantities  of  falling  water. 
Nor  is  there  a  whirlpool  action  in,  nor  rising  from,  the  body  proper  of 
the  ocean.  The  way  the  spray,  caught  and  drawn  up,  looked  at  times, 
easily  explained  to  me  how  this  delusion  originated. 

The  surprising  tranqutlity  of  the  clouds  shows  that  such  currents  of 
wind  need  not  be  of  great  height,  ht  least  not  at  their  borders,  where 
alone  such  whirls  can  take  place.  That  the  spouts  scarcely  shifted  their 
position  is  proof  that  the  velocity  of  the  concurrent  winds  was  almost 

4Of  course  this  was  not  the  "  cloud-burst  "  of  technical  meteorology, 
for  that  is  simply  an  unusual  excessive  rainfall.  — EDITOR. 


JULY,  1906. 


MONTHLY  WEATHER  REVIEW. 


313 


equal.  It  is  certain  that  this  velocity  can  not  have  been  great.  Several 
small  vessels  in  close  proximity  at  the  time  report  that  there  were  a  great 
noise  and  gusts  of  wind  in  the  immediate  vicinity  of  the  display,  while 
beyond  this  there  was  almost  a  dead  calm  (Boston  Globe,  September  1). 
This  latter  statement,  however,  seems  to  be  somewhat  exaggerated. 


The  following  is  a  list  of  the  photographs  and  the  times 
when  they  were  taken: 


SECOND  APPEARANCE. 


THE  PHOTOGRAPHS. 

We  have  to  acknowledge  our  debt  to  the  photographers  who 
happened  to  be  in  the  neighborhood  of  Cottage  City  on  Au- 
gust 19,  1896,  for  an  admirable  series  of  pictures  which  cover 
the  most  important  features  of  the  phenomenon.  Messrs.  Bald- 
win Coolidge,  146  Tremont  street,  Boston,  Mass;  J.  N.  Cham- 
berlain, Cottage  City;  F.  W.  Ward,  16  Adams  street,  Burling- 
ton, Vt. ;  Dodge,  of  Bangor,  Me.;  and  E.  K.  Hallet,  through 
Mr.  Coolidge  have  placed  their  photographs  in  the  care  of 
the  Weather  Bureau  for  study,  and  our  thanks  are  hereby 
extended  to  these  gentlemen  for  their  courteous  contributions 
to  the  available  scientific  data  that  have  come  into  our  posses- 
sion. Both  Coolidge  and  Chamberlain  were  stationed  on  the 
bluff  at  Cottage  City,  and  had  a  clear  view  over  the  ocean  to 
the  waterspout;  Mr.  Ward  stood  near  the  foot  of  Hope  avenue, 
in  Falinouth  Heights;  Mr.  Dodge  was  at  the  head  of  Vineyard 
Haven  Harbor  and  saw  the  spout  across  the  headland  near 
East  Chop  light;  Mr.  Hallet  was  on  the  high  ground  west  of 
Cottage  City.  These  locations  are  shown  on  the  chart,  fig.  25. 
Some  other  photographs  were  taken  on  a  small  scale  which 
contributed  somewhat  to  the  information  contained  in  those 
reproduced  in  this  memoir. 

The  first  appearance  of  a  waterspout  began  at  12:45  p.  m. 
and  ended  at  12:58  p.  m. ;  no  photographs  were  made  of 
this  phenomenon,  as  it  required  time  to  bring  the  cameras  into 
operation.  Mr.  Coolidge  was  half  a  mile  away  from  his  studio, 
at  home  for  dinner,  when  this  spout  appeared;  he  started  to 
secure  his  instrument,  when  unfortunately  the  spout  disap- 
peared. He  was  ready  on  the  bluff  for  the  second  appearance, 
which  began  at  1:00  p.  m.  and  ended  at  1:18  p.  m.  He  used 
a  rapid  symmetrical  Ross  lens,  with  a  focal  length  14|  inches 
from  the  diaphragm  to  the  ground  glass,  or  13|  inches  from 
the  back  of  the  lens  to  the  ground  glass.  Mr.  Chamberlain 
brought  his  camera  from  his  studio  to  the  edge  of  the  park, 
about  200  yards  from  the  water,  and  his  pictures,  therefore, 
include  a  foreground  showing  several  telegraph  poles.  The 
measured  distances  between  these  objects  give  the  scale  of 
the  photograph,  which  becomes  more  valuable  on  this  ac- 
count He  used  a  large  camera,  No.  5  euroscope,  with  equiva- 
lent focus  of  17£  inches  from  the  optical  center  to  the  sensitive 
plate,  and  a  lens  of  3-J-  inches  diameter.  These  sets  of  photo- 
graphs by  Coolidge  and  Chamberlain  both  show  a  schooner 
which  was  sailing  southeastward,  and  the  positions  of  the 
schooner  relative  to  the  waterspout  in  its  successive  positions 
are  very  useful  in  determining  the  time  intervals  between  the 
successive  pictures.  One  of  Chamberlain's,  fig.  27,  also  shows 
the  Succonesset  Shoal  light-ship,  together  with  the  waterspout 
near  it,  and  this  is  important  in  identifying  the  direction  of 
the  sight  lines  from  Cottage  City.  Mr.  Ward's  picture  was 
taken  with  an  Anthony  kodak  triad  camera,  4|  inches  focal 
length,  and  the  plate  is  4  by  5  inches;  this  was  enlarged  by 
Coolidge  to  the  8  by  10  size.  It  shows  the  cloud  formation 
and  is  most  instructive  as  to  general  meteorological  conditions; 
it  also  shows  the  curvature  of  the  vortex  tube  at  right  angles 
to  the  view  from  Cottage  City,  where  it  seemed  nearly  straight, 
as  seen  in  perspective  during  the  second  appearance.  Mr. 
Dodge  caught  a  distant  view  of  the  spout,  and  his  picture  also 
shows  the  great  cumulo-nimbus  cloud  from  which  it  descended ; 
his  sight  line  passed  just  to  the  south  of  the  East  Chop  light- 
house, and  this  distinctly  identifies  the  direction  of  the  spout 
at  that  time.  Ballet's  picture  was  taken  with  a  small  camera, 
but  shows  the  large  cumulo-nimbus  cloud  so  well  that  I  have 
taken  it  as  the  basis  of  the  thermodynamic  computations. 


Fig. 

No. 

Serial  No.  of 
photograph. 

27 
28 

1 
2 

29 

3 

30 

4 

31 

5 

82 

6 

33 

7 

ase. 

Photographer. 

Moment  of 
exposure. 

Photogra- 
pher's 
numeration 
of  negative. 

2d  A 

Chamberlain  

1:02  p.  in. 

2d  B 

1-OJ  p  m 

7933 

M  C 
2d  I) 

Hs.Het    

1:08  p.  m. 
1-12  p  m 

2d  E 
2d  F 

Ward  
Cooli.lge  

1:14  p.m. 

7934 

2d  G 

Coolidge 

1*17  p-  ni 

7936 

THIRD  APPEARANCE. 


34 

8 

3d  A 

Chamberlain  

1:20  p.m. 

35 

9 

3d  B 

Chamberlain  

1:24  p.m. 

36 

10 

3d  C 

Coolidge 

7935 

Notes  on  the  photographs. 

No.  1.  See  fig.  27. — Chamberlain,  %d  A,  at  1:02  p.  m.,  showing 
the  waterspout  5.75  miles  away,  the  lower  face  of  the  cloud  in 
great  detail,  the  foreground,  the  schooner  about  two  miles  out, 
and  Succonesset  Shoal  light-ship  about  eight  miles  distant; 
the  latter  can  be  seen  on  the  horizon  about  one  third  of  the 
apparent  distance  from  the  spout  to  the  schooner. 

No.  2.  See  tig.  28. — Coolidge,  2d  B,  at  1:03  p.  m.,  includes 
the  Marthas  Vineyard  steamer,  the  spout  and  cloud  in  nearly 
the  same  condition  as  shown  by  2d  A. 

No.  3.  See  fig.  29.— Hallet- Coulidge,  2d  C,  at  1:08  p.  m.  This 
picture  is  attributed  to  E.  K.  Hallet,  photographer,  and  is 
copyrighted  by  Baldwin  Coolidge,  Boston,  Mass.,  1897.  It 
seems  to  be  somewhat  later  than  2d  B  because  the  vortex  is 
leaning  more  toward  the  south,  in  accordance  with  the  drift 
of  the  cloud  stratum,  which  is  brought  out  more  positively  in 
the  third  appearance,  1:20  to  1:25  p.  m. ;  it  also  gives  us  the 
dimension  of  the  upper  cloud  which  is  not  seen  in  the  pictures 
2d  A,  2d  B.  Such  small-scale  photographs  of  the  whole  cloud 
region  serve  admirably  to  supplement  the  details  to  be  found 
only  on  the  large-scale  pictures,  and  should  always  be  made 
if  possible  by  those  having  kodaks  at  hand. 

No.  4.  See  fig.  30.— Dodge,  3d  D,  at  1:12  p.  m.,  is  chiefly  of 
importance  in  locating  the  line  from  the  head  of  Vineyard 
Haven  Harbor  to  the  waterspout.  The  curvature  toward  the 
southwest  in  the  center  begins  to  be  seen  from  that  angle  I 
estimate  that  this  was  taken  at  1:12  p.  m.,  though  there  may 
be  some  doubt  about  the  exact  minute. 

No.  5.  See  fig.  31. — Ward-Coolidge,  2d  E,  probably  at  1:14 
p.  m.,  taken  by  F.  W.  Ward,  enlarged  and  copyrighted  by  Bald- 
win Coolidge.  The  curvature  of  the  tube  is  now  fully  seen 
from  Falmouth  Heights,  where  this  plate  was  taken,  this  sight 
line  being  nearly  at  right  angles  to  those  from  Cottage  City. 
The  vortex  column  appeared  vertical  at  Cottage  City,  but 
strongly  curved  at  Falmouth  Heights  with  convexity  toward 
the  southwest.  In  the  third  appearance  the  convexity  is  seen 
nearly  broadside  on  at  Cottage  City,  and  this  indicates  some 
change  in  the  drift  of  the  lower  surface  of  the  cloud  relative 
to  the  layer  of  air  at  the  water.  This  photograph  gives  the 
horizontal  extent  of  the  cloud.  The  Hallet  photograph,  fig. 
29,  2d  C,  shows  the  precipitation  in  the  thunderstorm  preced- 
ing the  waterspout  by  about  one  mile. 

No.  6.  See  fig.  32. — Coolidge,  2d  F,  at  1:15  p.  m.,  shows  the 
enlargement  of  the  tube  before  breaking  up,  the  spray  being 
cast  out  from  all  parts  of  the  tube,  especially  at  the  top,  thus 
causing  the  conical  form. 

No.  7.  See  fig.  33.— Coolidge,  2d  G,  at  1:17  p.  m.,  gives  the 
phenomenon  at  the  breaking  up  of  the  second  appearance,  and 
it  locates  the  schooner  well  up  to  the  place  of  the  vortex. 

There  are  three  photographs  of  the  third  appearance. 


314 


MONTHLY  WEATHEB  REVIEW. 


JULY,  1906 


No.  8.  See  tig.  34. — Chamberlain,  Sd  A,  at  1:20  p.  m.,  shows 
the  top  of  the  vortex  advanced  toward  the  south  relative  to 
the  base,  indicating-  the  drift  in  the  cloud  stratum.  The 
schooner  has  moved  beyond  the  base  of  the  waterspout  and  is 
between  the  two  telegraph  poles;  a  tow  of  barges  is  just  com- 
ing into  view  on  the  extreme  right  of  the  photograph. 

No.  9.  See  fig.  35. —  Chamberlain,  3d  11,  at  1:24  p.  m.,  is  simi- 
lar to  the  preceding,  but  the  base  of  the  spout  has  moved 
toward  the  southeast;  the  schooner  and  the  barges  are  ap- 
proaching each  other. 

No.  10.  See  fig.  36.— Coolidge,  3d  C,  at  1:27  p.  m.,  is  a  later 
phase  of  the  third  appearance,  with  the  schooner  and  head  of 
the  tow  nearly  in  the  same  line.  The  schooner  is  about  two 
and  one-half  and  the  barges  about  three  miles  distant  from 
Cottage  City. 

POSITION    OF    THE    WATERSPOUT    IN    THK    SOUND. 

It  will  be  seen  that  from  the  foregoing  notes,  the  photo- 
graphs, and  the  chart  we  have  considerable  data  with  which 
to  find  the  position  of  the  waterspout  in  Vineyard  Sound.  It 
will  be  best  first  to  fix  our  attention  upon  the  first  part  of  the 
second  appearance  as  shown  in  the  photograph,  Chamberlain, 
2d  A,  fig.  27,  taken  at  about  1:02  p.  m.  My  own  personal 
survey  of  the  ground  gives  the  following  distances  approxi- 
mately, as  plotted  in  fig.  26.  The  telegraph  poles  are  marked 
1,  2,  3,  4,  and  Chamberlain's  camera  is  marked  5.  We  have  the 
distances,  5-1=450  feet,  5-4=504  feet,  1-2=72  feet,  2-3=120 
feet,  3-4=66  feet,  4-1  =  132  feet.  The  sight  line  to  the  water- 
spout is  laid  down,  also  that  to  the  schooner;  the  angular 
distance  between  them  is  5.44°.  On  photograph,  Chamberlain, 
2d  A,  fig  27,  is  also  shown  the  Succonesset  Shoal  light-ship, 
which  appears  as  a  dot  on  the  horizon  about  one-third  the  dis- 
tance from  the  foot  of  the  spout  to  the  schooner.  This  enables 
us  to  orient  the  entire  drawing  with  great  accuracy.  These 
lines  are  now  transferred  to  the  chart  of  Vineyard  Sound,  pub- 
lished by  the  U.  S.  Coast  and  Geodetic  Survey  as  No.  112, 
August  1901,  of  which  a  portion  is  reproduced  as  tig.  25. 

On  photograph,  Dodge,  2d  D,  fig.  30,  taken  from  the  head  of 
Vineyard  Haven  Harbor,  the  spout  is  shown  just  to  the  south 
of  East  Chop  light-house,  and  that  line  is  added  to  the  chart. 
The  spout  was  also  seen  from  Woods  Hole  at  the  head  of  Little 
Harbor,  and  a  measurement  of  the  line  as  described  gives  mag- 
netic declination  S.  75°  E.,  which  is  also  drawn.  It  was  seen 
from  Edgartown,  10°  east  of  true  north,  by  one  report,  this 
line  being  indicated  on  the  chart,  fig.  25. 

Dr.  George  Faulkner's  family  saw  the  second  appearance  from 
their  residence  near  the  water  in  the  town  of  Falmouth,  and 
their  sight  line  passed  just  south  of  the  steamboat  wharf 
at  Falmouth  Heights.  This  enables  us  to  fix  another  line  as 
shown  on  the  chart.  These  lines  all  converge  quite  accurately 
to  a  point  a  little  south  of  east  of  L'Hornmedieu  Shoal,  where 
other  observers  also  placed  it  by  estimate,  and  I  have  accord- 
ingly cut  off  the  Chamberlain  line  of  sight  at  that  point  on  my 
chart,  fig.  25.  This  makes  the  distance  from  Chamberlain  to 
the  waterspout  5.75  miles,  and  to  the  Succonesset  Shoal  light- 
ship eight  miles;  as  the  schooner  was  in  the  usual  inside  chan- 
nel it  was  about  two  miles  distant,  as  shown  on  this  same  chart. 
It  is  instructive  to  note  that  some  spectators  imagined  the 
spout  to  have  been  more  than  twenty  miles  from  Cottage  City. 
It  is  of  great  importance  to  be  able  to  accurately  convert  the 
distances  shown  on  the  photographs  into  angles,  because  the 
angles,  combined  with  the  length  of  the  sight  line,  give  the 
corresponding  linear  dimensions  at  the  spout  and  at  the 
schooner.  We  have  to  measure  the  linear  distance  on  this 
photograph  from  the  middle  of  the  schooner  to  the  middle  of 
the  waterspout,  which  is  48  millimeters  on  fig.  27,  Chamber- 
lain, 2d  A;  at  the  same  time  the  angular  distance  between  the 
sight  lines  from  the  camera  to  these  two  objects  is  found  from 
the  survey  to  be  5.44°.  This  was  determined  by  plotting  the 


lines  of  the  survey  on  a  large  scale,  and  testing  the  result  by 
numerous  checks  on  the  other  distances  measured  on  the  pho- 
tographs. Hence,  1  millimeter  =  6'  48"  of  angle.  This  is  th<- 
fundamental  dimension,  and  it  leads  to  1  millimeter  =  60 
feet  =  18.3  meters  at  the  waterspout. 

DIMENSIONS    AS    MKASCHEI)    ON    I'HOTOdKAl'H    2l>    A,    FIG.    27. 

By  this  process  we  obtain  the  absolute  dimensions  given  in 
the  accompanying  table. 

Distance  from  middle  of  schooner  to  middle  of  waterspout 
on  the  horizon,  measured  on  the  photograph,  48  mm. 

Angular  distance  subtended  by  the  sight  lines  at  th< 
camera,  as  determined  by  the  local  survey,  5.44°. 

Hence,!  mm.  subtends  5.44°  H- 48=  0.1133°=  6.80'  =  6'48". 


I'Y.  i. 

Heten, 

0  3014 

10  444 

•>0  888 

60  00 

tV  7 

19111 

*:t  <; 

240 

720 

'2W  '111 

4"'0 

144 

t.H    .S'l 

840 

256  O'i 

3GOO 

lu  -7  8 

Approximate  height  of  the  t«»p  uf  thr  Homl  (from  '.id  <.',  fig.  29)  ..  . 

1GOOO 

4876.8 

The  distance  moved  by  the  waterspout  from  the  beginning 
of  the  first  appearance  at  12:45  p.  in.  to  the  end  of  the  third 
appearance  at  1:28  p.  m.  can  be  found  as  follows: 

The  positions  of  the  schooner  and  the  waterspout  at  the  time 
of  taking  Chamberlain's  three  photographs  are  shown  on  the 
chart  (see  fig.  25),  as  nearly  as  can  be  determined;  2d  A,  at  1 :02 
p.  m. ;  3d  A,  at  1:20  p.  m. ;  3d  B,  at  1:24  p.  m.  In  the  inter- 
val, 1:02  to  1:24  p.  m.,  22  minutes,  the  schooner  moved  about 
0.65  mile.  This  is  at  the  rate  of  1.7  miles  per  hour.  The 
schooner  was  sailing  nearly  east-southeast,  and  the  sails  were 
set  to  catch  a  wind  from  the  northwest.  The  wind  was  very 
light  at  the  time,  as  stated  by  several  observers,  and  as  is  shown 
on  the  photographs  by  the  smoothness  of  the  water.  In  the 
interval,  12:45  to  1:28  p.  m.,  43  minutes,  the  vessel  passed  over 
the  distance  1.27  miles.  Similarly,  the  waterspout  passed  over 
the  distance  0.4  mile  in  the  interval,  1:02  to  1:24  p.  m.,  and  over 
the  distance  0.78  mile,  or  4018  feet,  in  the  interval,  12:45  to  1:28 
p.  m.,  while  the  whole  phenomenon  was  in  evidence.  This  is 
at  the  rate  of  1.10  miles  per  hour. 

It  is  instructive  to  compare  these  results  with  the  estimated 
dimensions  and  distances  as  reported  by  different  spectators. 
Mr.  Hanes  estimated  the  eastward  progress  as  2  miles,  diame- 
ter from  100  to  300  feet,  height  4000  to  5000  feet.  Mr.  North 
made  the  distance  of  the  waterspout  from  Cottage  City  20 
miles,  or  more,  supposing  that  the  foot  of  the  vortex  \vas  be- 
yond the  horizon,  and  that  from  his  view-point  the  base  of  the 
tube  was  20  feet  above  the  sea  level;  he  made  its  eastward  move- 
ment about  equal  to  its  own  height  before  it  disappeared,  which 
is  nearly  correct,  and  called  this  one  mile.  Mr.  Coolidge. 
October  19,  1896,  estimated  the  height  of  the  spout  at  from 
6000  to  10,000  feet,  or  21  to  28  times  its  diameter,  and  the 
latter  at  300  to  375  feet  and  the  distance  8  miles.  Mr.  Cool- 
idge, September  1,  1897,  made  it  400  to  600  feet  in  diameter 
at  its  mid-height,  from  4000  to  6000  feet,  or  perhaps  10,000 
feet  high,  and  5  miles  distant.  The  observers  on  the  yacht 
Avalon,  which  was  very  near  the  waterspout,  made  the  diame- 
ter 100  feet.  Mr.  E.  H.  Garrett  estimated  over  300  to  nearly 
500  feet  high,  and  125  feet  in  diameter;  Mr.  John  B.  Garrett: 
6  miles  distant,  height,  750  feet;  diameter,  125  feet;  height  of 
cascade,  125  feet;  Mr.Abbott;  height,  3000  to  4000  feet. 

[The  treatment  of  this  waterspout  will  be  continued  in  Sec- 
tions VII,  VIII,  and  IX.] 


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AUGUST,  1906. 


MONTHLY  WEATHER  REVIEW. 


360 


STUDIES  ON  THE  THERMODYNAMICS  OF  THE  ATMOS- 
PHERE. 

By  Prof.  FRANK  H.  BIOELOW. 

VII  —THE  METEOROLOGICAL  CONDITIONS  ASSOCIATED  WITH 
THE  COTTAGE  CITY  WATERSPOUT. 

The  data  that  have  been  collected  regarding  the  meteoro- 
logical conditions  prevailing  at  the  time  of  the  Cottage  City 
waterspout  are  sufficiently  extensive  and  accurate  to  enable  us 
to  study  carefully  the  causes  that  produced  the  phenomenon, 
and  to  derive  several  important  results  regarding  the  forma- 
tion of  lofty  cumulo-nimbus  clouds  and  the  dynamic  actions 
going  on  within  them.  In  this  instance  we  can  compute 
approximately  the  forces  producing  the  ascension  of  the 
buoyant  vapor  in  the  cloud,  the  formation  of  hail  and  the 
energy  working  in  the  vortex  at  the  base  of  the  cloud  which 
developed  as  the  waterspout.  I  shall  proceed  to  give  these 
facts  in  detail,  as  this  computation  may  serve  as  a  type  to  be 
followed  in  discussing  other  cases  of  similar  local  atmospheric 
action. 

Besides  the  formation  and  dissipation  of  the  tube,  noted  in 
the  several  reports  and  shown  in  figures  27-36,  there  are 
special  features  to  which  attention  must  be  directed:  (1)  In 
the  third  appearance  the  vortex  tube  shows  a  gradual  tapering 
of  the  form  from  the  cloud  to  the  sea  level,  but  in  the  second 
arjpearance  the  tube  seems  to  have  about  the  same  diameter 
from  the  cloud  to  the  sea  level.  It  is  necessary  to  account 
for  this  divergence  in  the  type.  (2)  The  photographs  show 
a  peculiar  set  of  boundary  curves  in  the  cloud  level  which 
depend  upon  certain  dynamic  forces  that  we  shall  attempt  to 
discover.  (3)  At  the  foot  of  the  tube,  near  the  sea  level,  there 
was  a  great  commotion  of  the  waters,  with  a  white  nucleus 
just  under  the  tube,  and  finally  a  beautiful  cascade  of  imposing 
dimensions  surrounding  it.  These  are  topics  of  especial 
interest  besides  those  usually  considered  in  discussing  such 
vortices. 

The  meteorological  conditions  are  given  quite  fully  by  the 
regular  observations  of  the  neighboring  Weather  Bureau  sta- 
tions, Nantucket  being  a  station  of  the  first  order  and  having  a 
continuous  barograph  and  thermograph  record ;  Woods  Hole, 
a  station  of  the  second  order,  with  complete  daily  evening 
observations;  and  Vineyard  Haven,  a  station  of  the  third  order, 
with  daily  temperature,  wind,  and  cloud  reports.  The  daily 
weather  map  of  8  a.  m.,  August  19,  1896,  exhibits  the  general 
conditions  for  the  United  States,  and  from  it  can  be  obtained 
the  local  conditions  prevailing  at  that  hour,  at  least  approxi- 
mately. The  physical  appearance  of  the  waterspout  has  been 
described  fully  in  the  reports  already  given,  and  there  is  also 
a  series  of  notes  of  which  further  use  will  be  made  in  the 
proper  places.  We  shall  endeavor  in  this  Section,  VII,  to 
discuss  the  scientific  problems  which  are  naturally  suggested 
by  these  data,  with  the  view  of  illustrating  typical  methods  of 
treating  waterspout  and  tornado  phenomena  whenever  these 


Clear  during  the  forenoon,  partly  cloudy  during  the  afternoon.  Thun- 
derstorm: thunder  first  heard,  1:58  p.  m.;  loudest,  3:02  p.  m.;  last,  3:50 
p.  m.  Storm  came  from  the  northwest  and  moved  toward  the  southeast; 
temperature  before  the  storm  66°,  after  67°;  direction  of  the  wind  before 
the  storm  northwest,  after,  northwest;  during  the  storm  the  wind  shifted 
to  the  northeast.  Rain  began  2:55  p.  m.;  ended  3:20  p.  m.;  amount  0:33 
inch.  Maximum  wind  velocity  38  miles  per  hour  from  the  northwest,  at 
3:00  p.  m.  A  few  hailstones  fell  about  3:10  p.  m.,  and  quite  a  heavy  fall 
of  hail  was  reported  a  few  miles  north  of  this  office. 

The  weather  map  of  August  19,  1896,  is  represented  as 
fig.  37. 

In  Section  A  of  Table  50  the  meteorological  data  are  given 
for  Woods  Hole,  Vineyard  Haven,  and  Nantucket  on  August 
19,  1896.  They  are  extracted  from  Forms  1001-Met'l.  of 
Woods  Hole  and  Nantucket,  and  Form  1004-Met'l.  of  Vine- 
yard Haven.  The  notation  is  as  follows:  B=  barometric  pres- 
sure; <=dry-bulb  thermometer;  <j=wet-bulb  thermometer; 
d=  dew-point;  R.  H.  =  relative  humidity;  e=  vapor  tension; 
Max.  t  and  Min.  £=  maximum  temperature  and  minimum  tem- 
perature for  the  periods  ending  at  the  respective  times  of 
observations;  Dir.  =  direction  and  Vel.=velocity  of  the  wind; 
Amt.= amount  of  precipitation;  Amt.= amount;  Kind;  Dir.= 
direction  from  which  the  clouds  came;  Local  tirne=hour  of 
making  the  regular  observations. 

In  Section  B  are  given  the  meteorological  data  at  the  even- 
ing observation  for  ten  days  immediately  preceding,  and  ten 
days  immediately  following  the  date  August  19, 1896,  with  the 
purpose  of  showing  the  kind  of  August  weather  prevailing  in 
that  locality. 

In  Section  C  are  given  data  at  alternate  hours  obtained  from 
the  continuous  self-register  of  the  pressure  and  the  tempera- 
ture for  Nantucket  during  August  19,  1896. 

PROBABLE  CONDITIONS  NEAR  THE  WATERSPOUT. 

The  general  chart  for  August  19, 1896  fig.  37,  shows  that  an 
area  of  high  pressure  was  central  over  the  upper  Lake  region, 
with  its  eastern  edge  just  overlapping  the  southern  New  Eng- 
land coast.  This  anticyclone  was  advancing  quite  rapidly 
for  the  summer  season,  and  on  the  following  day,  August  20, 
it  extended  far  eastward  over  the  ocean.  The  winds  were 
light  to  fresh  from  the  north  and  northwest  over  New  Eng- 
land, and  the  advancing  border  of  the  area  of  high  pressure 
produced  a  showery  condition  with  precipitation  in  eastern 
Maine,  the  upper  St.  Lawrence  Valley,  and  on  the  Massachu- 
setts coast.  Later  in  the  day  several  thunderstorms  developed 
in  the  neighborhood  of  Vineyard  Sound,  such  storms  being 
reported  as  follows,  seventy-fifth  meridian  time: 


occur. 


METEOROLOGICAL    CONDITIONS   FOR    AUGUST  19,    1896. 


Vineyard  Haven,  Marthas  Vineyard,  Mass. — The  Journal  for 
this  station  has  been  given  as  the  report  of  W.  W.  Neifert,  the 
observer,  in  the  preceding  Section,  VI,  page  307,  extract  A. 

Nantucket,  Mass. — The  Journal  for  this  station  has  been 
given  as  the  report  of  Max  Wagner,  the  observer,  on  page  307, 
extract  C. 

Woods  Hole,  Mass.  —  The  report  for  this  station  has  been 
given  as  the  report  of  J.  D.  Blagden,  the  observer,  on  page 
307,  extract  D. 

This  last  report  also  adds: 


Station. 

Began. 

Loudest. 

Ended. 

Precipitation. 

Wood  s  Hole. 

1-58  p.  m. 

3:02  p.  m. 

3:5X1  p.m. 

2:55  to  3:20  p.  m.  ;  0.  33  inch. 

1:45  p.m. 

3:04  p.m. 

3:45  p.  m. 

3:04  to  3:30  p.  m.;  0.88  inch. 

2:40  to  4:00  p.  m.;  0.03  inch. 

*Nole  by  observer  at  Nantucket,  Mats.—  An  ordinary  thunderstorm  was  already  passing 
across  the  sound,  when  about  12:40  p.  m.  a  huge  black  tongue  shot  down  from  an  alto- 
cumulus cloud  that  floated  half  a  mile  high  at  me  northern  edge  of  the  shower. 

Several  observers  mention  the  thunderstorm  that  occurred 
in  the  neighborhood,  in  connection  with  the  formation  of  the 
waterspout  at  the  base  of  a  large  cumulo-nimbus  cloud.  The 
day  had  been  generally  calm,  the  breeze  being  about  three  to 
six  miles  per  hour  from  the  northwest.  There  was  a  pro- 
nounced turbulent  congestion  of  the  atmosphere  along  the 
southeastern  edge  of  the  anticyclone,  also  a  strong  convec- 
tional  movement  in  the  vertical  direction,  as  was  indicated  by 
the  rapid  formation  of  clouds,  the  production  of  precipitation, 
and  the  generation  of  thunderstorms  accompanied  by  an  over- 
turning of  the  strata.  All  these  are  consequences  attending 
the  flow  of  cold  anticyclonic  air  over  the  ocean,  causing  ab- 
normal temperature  stratifications  to  be  superposed  upon  the 
ordinary  quiet  arrangement  due  to  solar  insolation  taken  by 
itself.  The  readjustment  of  the  thermal  equilibrium,  which 
had  become  much  congested,  gave  rise  to  the  phenomena 


361 


MONTHLY  WEATHER  REVIEW. 


AUGUST,  1906 


37. — Weather  conditions,  Wednesday,  August  19,  IbMb,  at  8  a.  m.,  seventy-tilth  meridian  time,  preceding  the  waterspout. 


observed  on  the  occasion,  one  of  which  was  the  formation  of 
the  waterspouts  from  the  base  of  the  same  thunderstorm  cloud. 
The  vertical  convection  producing  the  cloud  became  vigorous 
enough  to  generate  vortex  tubes  during  the  interval,  12:45  to 
1:28  p.  m.  Similar  violent  disturbances  of  the  lower  atmos- 
phere occur  in  summer  whenever  masses  of  air  of  very  differ- 
ent densities  are  brought  close  together,  with  abrupt  changes 
in  the  temperatures  within  short  distances.  In  the  Missis- 
sippi Valley  this  usually  occurs  in  the  southeast  quadrant  of 
a  cyclone,  where  the  two  streams  flow  together  or  overflow 
one  another,  one  cool  and  dry  from  the  northwest,  the  other 
warm  and  moist  from  the  south.  Near  the  Atlantic  coast  the 
same  effect  is  produced  by  an  anticyclonic  area  with  dry,  cool 
northwest  winds  pushing  forward  and  protruding  the  current, 
flowing  freely  in  the  higher  levels,  over  the  warm,  moist  layers 
of  air  lying  near  the  surface  of  the  ocean.  In  all  such  cases 
we  have  a  natural  thermodynamic  engine,  where  the  pressure, 
volume,  temperature  (pv  vlt  Ts )  for  the  "  source  "  of  the  ther- 
mal energy  is  quite  different  from  (/)„,  u0,  T0)  for  the  "sink", 
the  former  corresponding  with  the  boiler  and  the  latter  with 
the  condenser  of  an  engine.  Thus,  (pv  vv  Tl )  apply  to  the 
meteorological  conditions  in  the  warm  air  over  the  ocean 
before  the  anticyclone  disturbs  it,  and  (pa,  v0,  Ta)  to  the  con- 
ditions prevailing  in  the  cool  air  of  the  anticyclone  itself. 
The  motions  of  the  atmosphere,  which  result  in  clouds,  thun- 
derstorms, and  waterspouts  simply  represent  the  stream  lines 
through  which  the  air  flows  in  restoring  the  abnormal  tem- 
peratures to  equilibrium.  In  nature  there  is  a  tendency  to 
produce  a  succession  of  such  thermal  engines  throughout  the 
atmosphere,  first  on  a  large  scale  due  to  solar  radiation,  with 
the  boiler  along  the  Tropics,  and  the  condenser  around  the 


poles;  second  on  a  small  scale,  wherever  in  the  local  circula- 
tions, which  are  secondaries  derived  from  the  first  kind, 
masses  of  air  of  different  temperatures  come  into  close  juxta- 
position. Similar  processes  continue  from  step  to  step,  from 
the  general  circulation  on  the  entire  hemisphere  of  the  earth, 
to  the  smallest  whirl  that  occurs  in  the  turbulent  internal  vor- 
tex motions  of  the  air. 

Were  it  possible  to  trace  the  course  of  these  stream  lines 
throughout  such  congested  masses  as  are  in  motion  in  torna- 
does and  thunderstorms,  we  should  be  able  to  study  many 
interesting  problems  in  hydrodynamics  as  well  as  in  thermo- 
dynamics. 

Examining  the  meteorological  data  I  make  the  following 
deductions.  The  temperature  at  the  base  of  the  waterspout  was 
about  67.5°.  This  is  the  maximum  temperature  of  the  day, 
and  the  thermograph  for  Nantucket  shows  that  the  waterspout 
occurred  at  the  time  of  maximum  temperature,  just  before  the 
break  in  weather  occurred.  It  then  fell  to  about  56.5°  at 
Vineyard  Haven,  and  59.0°  at  Woods  Hole  and  Nantucket,  so 
that  the  effective  temperature  in  the  anticyclone  was  about  58.0°. 
Hence  we  shall  assume  <,=  67.5°  F.  and  <0=58.0°  F.  The 
pressure  in  the  anticyclone  may  be  taken  30.10,  and  on  the  ocean 
near  the  ivaterspout  30.05,  ivhich  is  only  a  little  lower.  The  table 
makes  the  relative  humidity  range  above  90  per  cent  at  Nan- 
tucket for  several  days  till  August  18.  By  the  morning  of 
August  19  a  decided  change  had  occurred,  in  which  the  rela- 
tive humidity  fell  nearly  to  60  per  cent.  At  Nantucket  it  was 
60  per  cent  at  8:20  a.  m.,  and  74  per  cent  at  8:20  p.  m.;  at 
Woods  Hole  it  was  61  per  cent  at  8:17  p.  m.  It  is  very  re- 
markable that  this  great  waterspout  was  produced  on  the  day 
when  the  lower  strata  of  the  atmosphere  were  drier  than  on  any  other 


AUGUST,  1906. 


MONTHLY  WEATHEE  REVIEW. 

(A)  TABLE  50.— Meteorological  data  for  August  19,  1896. 


362 


Station. 

Pressure. 

Temperature  and  moisture. 

Wind. 

Precipi- 
tation. 
Amt. 

Clouds. 

Local 
time  of 

observa- 
tion. 

£» 

1. 

%. 

d. 

R.H. 

e. 

Mai.  t. 

Min.  (. 

Dir. 

Vel. 

Amt. 

Kind. 

Dir. 

Inches. 

°f. 

Of_ 

Of, 

Per  cent. 

Inches. 

Of 

64.0 
67  4 

72.0 

64.0 
67.5 

°F. 
59.0 
64.0 

56.5 

59.2 
61.5 

Miletp.h. 

Inch. 

8:17  a.  m. 
8:17p.  m. 

8:17p.m. 

8:20  a.  m. 
8:20  p.m. 

Woods  Hole  \ 

30.15 

64.0 

56.2 

50.0 

61 

.360 

uw. 
nw. 

n. 
n. 

14 

0.33 
0.38 

0.02 
0.03 

0 

0 

0 

30.  03 
30.13 

64.0 
62.0 

56.5 
57.0 

51.0 
53.0 

62 
74 

.373 
.402 

10 

8 

few 
0 

Ci. 
0 

w. 

0 

(B)  Records  for  10  days  either  side  of  August  19,  1896. 


Dates. 

Woods  Hole,  8:17  p.  m. 

Nantucket,  8:20  p.  m. 

(. 

<l- 

d. 

E.H. 

e. 

Mai.  (. 

Min.  t. 

t. 

h- 

d. 

K.H. 

e. 

Max.<. 

Min./. 

0  F. 
73.0 
76.0 
76.7 
75.2 
72.5 
66.5 
65.2 
69.2 
68.8 
62.2 

610 

64.8 
65.0 
67.0 
71.0 
71.5 
65.0 
68.0 
68.0 
65.3 
64.0 

°  F. 
71.8 
71.5 
72.5 
73.0 
71.5 
66.0 
64.0 
67.0 
63.8 
58.2 

56.2 

59.0 
58.3 
61.0 
70.2 
69.0 
62.8 
65.0 
65.0 
58.8 
58.0 

°  F. 
72 
69 
70 
72 
71 
66 
63 
66 
61 
55 

50 

55 
54 
57 
70 
68 
62 
68 
63 
54 
54 

Per  cent. 
94 
80 
82 
90 
95 
98 
94 
89 
76 
79 

61 

71 
67 
71 
96 
88 
89 
85 
85 
68 
70 

Inches. 
.783 
.707 
.732 
.783 
.757 
.638 
.575 
.638 
.536 
.432 

.360 

.432 
.417 
.465 
.732 
.684 
.555 
.575 
.375 
.417 
.417 

Of 

78.2 
85.8 
87.0 
85.1 
81.9 
71.0 
69.0 
71.0 
77.7 
69.8 

67.4 

70.0 
71.0 
71.8 
73.3 
76.1 
75.7 
73.2 
73.8 
70.7 
68.0 

°F. 
72.2 
73.0 
75.0 
75.2 
72.5 
66.5 
65.0 
65.9 
68.5 
60.3 

610 

59.1 
64.5 
65.9 
68.2 
69.5 
64.0 
66.3 
67.0 
60.8 
62.9 

°  F. 
70.0 
72.5 
74.5 
71.0 
71.0 
66.0 
64.0 
65.0 
66.5 
64.0 

62.0 

59.5 
57.5 
64.5 
69.0 
67.5 
64.5 
64.0 
68.5 
61.5 
58.0 

°  F. 
70.5 
71.0 
72.5 
70.0 
70.0 
66.0 
63.5 
64.5 
64.5 
63.5 

57.0 

55.5 
56.5 
60.0 
68.0 
65.5 
64.0 
62.5 
67.0 
56.5 
56.0 

°F. 
71 
70 
72 
70 
70 
66 
63 
64 
64 
63 

53 

52 
66 
57 
68 
64 
64 
62 
66 
52 
55 

Per  cent. 
98 
93 
91 
95 
95 
100 
97 
97 
90 
97 

74 

78 
94 
77 
95 
90 
97 
92 
93 
74 
89 

Inches. 
.757 
.732 
.783 
.732 
.732 
.638 
.575 
.595 
.595 
.575 

.402 

.887 
.448 
.465 
.684 
.595 
.595 
.555 
.638 
.387 
.432 

Of 

78.0 
86.3 
83.2 
81.8 
82.0 
74.0 
67.5 
66.8 
74.2 
73  0 

67.6 

69.0 
68.5 
71.0 
74.6 
75.5 
74.8 
73.8 
74.0 
68.0 
68.8 

°F. 

70.2 
72.5 
74.5 
71.0 
71.0 
66.0 
64.0 
63.2 
66.5 
64.0 

61.6 

59.0 
57.5 
64.5 
66.1 
67.5 
64.0 
63.5 
63.3 
61.5 
58.0 

August  12  

August  18.          

August  19  

August  20  

August  22        

August  24                

A  ugust  26                    

August  28             

(C)  Continuous  self-register  of  pressure  and  temperature  at  Nantucket,  Mass.,  August  19,  1896. 


Hours  of  seventy-fifth  meridian  time. 

Mid't. 

2a.m. 

4  a.  m. 

6a.m. 

8a.m. 

10  a.  m. 

Noon. 

2p.m. 

4  p.  m. 

6  p.  in. 

8  p.m. 

10  p.m. 

Mid't. 

29  99 

29.97 

29.96 

30.00 

30  03 

30.05 

30.  OB 

30.05 

30.07 

30.09 

30.12 

30.15 

30.16 

61.0 

60.0 

61.0 

62.5 

64.0 

65.0 

66.0 

67.0 

63.0 

64.0 

63.0 

63.5 

63.0 

day  of  that  month.  A  comparatively  low  humidity  was  prevail- 
ing during  the  formation  of  the  vortex,  and  even  the  thunder- 
storms of  the  afternoon  did  not  avail  to  increase  it  much,  as 
it  rose  only  to  74  per  cent  in  the  evening.  There  was  no 
doubt  considerable  local  fluctuation  in  the  humidity  for  short 
intervals,  but  the  prevailing  anticyclone  lowered  the  humidity 
for  the  duration  of  two  or  three  days.  We  have  therefore  the 
special  problem  of  accounting  for  the  waterspout  during  con- 
ditions which  were  quite  the  reverse  of  those  usually  assumed 
to  prevail.  Tornadoes  are  usually  found  connected  with 
warm,  moist  air,  but  here  we  find  cool,  dry  air,  showing  that 
it  is  not  high  surface  temperature  and  humidity  alone  that 
causes  these  vortices.  After  several  trial  computations  on  the 
cloud  dimensions,  which  depend  upon  the  correct  surface 
data,  and  allowing  a  small  rise  in  the  humidity  percentage 
from  8:17  a.  m.  to  1  p.  m.  over  the  61  or  62  per  cent  prevail- 
ing at  the  early  hour,  I  have  concluded  to  accept  R.  H.=64 
per  cent  as  that  prevailing  near  the  surface  of  the  water  at  the 
time  the  waterspout  was  formed.  We  therefore  have  to  begin 
the  computations  with  the  following  data  for  the  air  just 
above  the  surface  of  the  water  at  1  p.  m. : 
B  =  30.05  inches, 
t  =  67.5°  F. 
R.  H.  =  64  per  cent. 

COMPUTATION    OF  THE    PRESSURE  B,  TEMPERATURE    t,  VAPOR-TENSION    6, 
AND    HEIGHT    H,    FOR    THE    a,    (1,    f,    S    STAGES. 

We  now  have  the  meteorological  data  at  sea  level  beneath 


the  cloud  which  surmounted  the  waterspout,  as  shown  in  the 
photograph  (fig.  29, 2d  C),  taken  at  about  1 :08  p.  m.,  by  Mr.  E.  K. 
Hallet.  This  cloud  is  a  large  cumulo-nimbus;  its  flat  base  is 
about  3500  feet  above  the  sea  level,  and  its  apex  about  three 
miles  high.  Upon  the  southern  extension,  on  the  right-hand 
side  of  the  plate,  there  is  a  thunderstorm  and  the  rain  is  falling 
freely;  the  northern  side  is  clearing,  and  there  seems  to  be 
sunshine  in  several  places;  from  the  midst  of  the  cloud  the 
waterspout  projects  down  to  the  sea  level.  At  the  top  of  the 
waterspout  tube  the  curvature  of  the  vortex  is  well  defined, 
and  at  the  bottom  there  is  a  fountain  of  water  surrounding  it 
in  a  circular  cascade.  We  shall  determine  as  accurately  as 
possible  the  meteorological  elements  (B,  t,  e)  at  the  base  of  the 
cloud,  that  is,  at  the  top  of  the  a-stage,  which  extends  from 
the  sea  level  to  the  lower  face  of  the  cloud,  and  expresses  the 
fact  that  this  stratum  of  air  is  composed  of  dry  air  and  invis- 
ible aqueous  vapor  mixed  in  certain  proportions,  as  indicated 
by  the  relative  humidity,  which  is  64  per  cent  at  sea  level  and 
100  per  cent  at  the  base  of  the  cloud.  We  shall  use  the 
notation : 

hv  Bv  tv  e,  at  the  top  of  the  a-stage,  or  the  base  of  the  cloud. 
h,  B,  t,  e  at  the  bottom  of  the  a-stage,  or  the  sea  level. 

Compare  the  notation  on  page  677  of  the  International 
Cloud  Report. 

(1)  The  working  formula  for  the  a-stage  is  No.  145,  as  given 
on  page  496  of  the  same  cloud  report: 


363 


MONTHLY  WEATHER  REVIEW. 


AUGOST,  1906 


C. 


!!„ 


Constant  =  U).2374+  0.1512  ^+0.0232-^)  log  T. 

-  (o.06858  +  0.02592  J  \  log  B  ........ 

where  T  is  the  absolute  temperature  =  273°  +  1°  centigrade. 
This  formula  is  reduced  to  the  numerical  Tables  94,  95,  96, 
pages  550  to  553  of  that  report,  inclusive,  the  T  and  B  terms 
being  summarized  by  Ca  =  I0  +  IIa  .  Some  examples  of  the 
use  of  these  tables  are  given  in  that  report  on  page  573  and 
following,  also  page  765  and  following,  the  accompanying 
text  having  the  necessary  precepts  for  practical  work.  They 
will  be  further  illustrated  in  the  examples  offered  by  this 
waterspout. 

(2)  The  /S-stage  extends  from  the  base  of  a  cloud  to  the  plane 
of  freezing  temperature,  t=  0°C.,  which  in  this  cumulus  cloud 
lies  at  about  2800  meters,  or  9200  feet,  above  sea  level,  so  that 
the  /9-stage  stratum  is  not  far  from  1700  meters  or  5600  feet 
thick.  In  the  present  case  the  «-stage  is  about  two-thirds 
of  a  mile  deep,  and  the  /9-stage  a  little  more  than  one  mile 
deep.  The  /3-stage  consists  of  a  mixture  of  dry  air,  invisible 
aqueous  vapor,  and  condensed  aqueous  vapor  in  the  form  of 
minute  water  drops  or  cloud  particles  which  reflect  and  refract 
the  light,  and  thus  make  the  cloud  appear  as  a  visible  mass  or 
a  region  of  condensation.  The  formula  for  the  /?-stage  is  No. 
146  as  given  on  page  496: 


=  Constant  =  (o.2374  +  0.4743  1  +  0.145 


(146) 


^ 


-    0.06858  -  0.04266        log  (B1  —  el) 


where  the  notation  is  taken  from  Table  133,  page  677,  of  the 
Cloud  Report.  The  numerical  tables  are  given  on  pages 
554  to  556  and  Tables  97,  98,  and  99  for  the  successive  terms, 
10  ,  Up  ,  IILj  ,  and  examples  of  the  computation  may  be 
found  on  pages  574,  696  and  following,  also  in  this  paper. 

(3)  The  f-stage  stratum  is  shallow,  in  this  case  only  75 
meters  or  246  feet  thick,  and  it  contains  the  layer  of  at- 
mosphere within  which  the  water  of  the  cloud  is  turning  to 
ice,  the  temperature  remaining  constant  at  the  freezing  point 
during  this  process.  In  this  layer  the  aqueous  content  is 
changing  its  physical  state,  though  not  its  temperature,  and 
there  is  only  a  mixture  of  aqueous  vapor,  water,  and  ice,  since 
there  is  no  thermal  change  in  the  dry  air  because  of  the  con- 
stant temperature,  the  cooling  by  expansion  just  balancing  the 
warming  due  to  evolution  of  latent  heat. 

This  is  a  very  interesting  process  and  will  be  referred  to 
again  in  a  later  section  of  this  paper.  The  formula  is  No.  147, 
on  page  496,  in  the  notation  of  the  Cloud  Report,  page  677: 


Cy=  Constant 


=  -  ^0. 


06858-0.04266  - 


log  (£„-*„) IIy 


(147) 


-(49.78^+18.82^, 


rv. 


The  table  for  IIy  is  the  same  as  Hg,  page  555,  and  those  for 
IIIT  and  IV  Y  are  given  on  page  557.  Numerical  examples  can 
be  found  on  page  575,  also  on  page  697  and  following;  like- 
wise compare  the  ^-stage  of  the  Cottage  City  waterspout,  later 
in  this  paper,  under  (o). 

(4 )  The  5-stage  relates  to  a  stratum  of  mixed  dry  air,  frozen 
aqueous  vapor,  i.  e.,  ice  vapor,  and  ice  or  snow  below  the  freez- 
ing temperature,  and  in  the  present  case  this  stratum  extends 
from  the  height  of  about  2880  meters,  or  9450  feet,  above  the 
sea  level  to  the  apex  of  the  cloud  which  is  not  far  from  4940 


meters,  or  16,200  feet;  so  that  the  <?-stage,  or  the  snow-stage, 
is  about  2060  meters,  or  6750  feet  in  depth,  that  is  about  one 
and  one-fourth  miles  thick.  The  formula  is  No.  148  on  page 
496,  in  notation  of  pages  677  or  678,  as  follows: 

,  =  Constant  =  H).  2374  +  0.4743      +0.145  31)  log  Tu 
(148) 


I, 


-    0.06858-0.04266        log  (#„-«„)  ....     II 


.III, 

The  numerical  tables  are  on  pages  555,  558,  and  559,  the 
table  for  II6  being  identical  with  that  for  ILj.  Examples  of 
the  frozen  or  (5-stage  may  be  found  on  pages  576,  697-712, 
also  in  the  following  computations  on  this  waterspout.  It  is 
convenient  to  have  a  distinct  notation  for  the  bottom  and  top 
of  each  of  these  four  stages,  and  this  is  done  in  the  notation 
of  pages  677  and  G78  of  the  Cloud  Report  by  simply  trans- 
ferring the  suffix  of  the  bottom  of  the  stage  to  the  place  of  an 
exponent  at  the  top  of  that  stage.  The  notation  for  the  top  of 
one  stage  is  equivalent  to  that  of  the  bottom  of  the  next  higher 
stage,  and  both  symbols  may  be  employed. 

In  the  computation  of  h,  B,  t,  e  for  the  several  stages  of  the 
Cottage  City  waterspout  explicit  directions  will  now  be  given 
for  each  stage  in  the  work,  for  the  sake  of  providing  suitable 
precepts  to  be  followed  by  others  pursuing  this  line  of  re- 
search,  and  in  order  that  the  several  steps  may  be  clearly  and 
accurately  understood.  The  tables  for  each  stage,  pages  550 
to  559,  were  all  computed  so  that  the  absolute  temperature, 
r  =  273°  +  <°C.,  which  appears  in  the  formula)  is  found  as  t°  C. 
in  the  argument  of  the  tables,  for  the  sake  of  convenience  in 
computing. 

(A)    THE  a-STAOE  OE  UNSATUKATED  PROCESS. 

The  sea-level  conditions  as  above  given  may  be  converted  into 
the  metric  system  by  the  following  table: 


English  sys- 
tem. 

Transferred  to  the  metric  system. 

Metric  system. 

B 

30.05  in 

By  Smithsonian  Table  64 

7fiQ  97  mm 

t    

67.  5°  F 

By  Smithsonian  Table  2 

19  72°  C 

Relative  humidity 

64  per  ct  . 

64  per  cent 

e    

By  Smithsonian  Table  43 

e  for    saturation    at 

19.72°,  Broch's  value,   is 

17.06  mm.  and  64  per  cent 

of  this  is— 

10.92  mm. 

e 
B 



10.92-:-  763.27=  

0.0143 

Reduction  of  ~ 

From    Table    136    p     690 

0  0013 

B  '  ' 
e 

Cloud  Report. 

Corrected  „  

0.0143  —  0.0013  — 

00130 

a 

The  result  of  the  discussion  of  the  value  of  the  ratio    ^   at 

the  sea  level  and  at  the  base  of  the  cumulus  cloud,  as  given 
on  pages  677  to  693  of  the  Cloud  Report,  was  to  show  that  the 

o 

ratio     D  at  the  sea  level  in  the  «-stage    has    a  larger  value 

than  at  the  base  of  the  cloud.  This  is  due  to  the  fact  that  in 
nature  the  atmospheric  process  does  not  exactly  follow  the 
adopted  theory  of  the  a-stage,  and  is  not  a  true  adiabatic 
process  as  the  formula  requires.  We  can,  however,  adapt  the 

formula  to  this  case  by  applying  to  the  sea-level  value  of  -„  a 

slight  correction  to  make  it  smaller  at  the  base  of  the  cloud, 
and,  as  the  outcome  of  a  very  extensive  discussion  of  this 
problem,  the  necessary  corrections  are  given  in  Table  136, 


AUGUST,  1906. 


MONTHLY  WEATHER  REVIEW. 


364 


page  690,  of  the  Cloud  Report  for  metric  measures,  and  on 
Table  18,  page  107,  of  the  Barometry  Report  for  English 
measures.  It  is  necessary  to  determine  this  ratio  quite  accu- 
rately for  close  computations  of  the  humidity  correction, 
according  to  the  theory  adopted  in  these  two  reports.  In 
this  connection  the  reader  is  referred  to  further  remarks  on 
this  formula,  which  has  been  in  use  since  1897  by  the  Weather 
Bureau,  as  found  on  page  781  of  Dr.  J.  Hann's  Lehrbuch  der 
Meteorologie,  1901,  and  on  page  30  of  the  Meteorologische 
Zeitschrif  t  of  January,  1903,  by  Dr.  J.  Liznar,  where  the  formulae 
are  proved  to  be  sufficiently  accurate  for  all  practical  compu- 

g 
tations.     The  Table  136  gives  for  the  argument  ,,  =  .0143  and 

the  assumed  approximate  height  of  the  base  of  the  cloud, 
1100  meters,  a  correction  which  I  take  as  —  .0013,  so  that  we 

a 

have  .0143  —  .0013  =  .0130  as  the  value  of  B  to  be  employed 

throughout  the  computation,  at  least  so  long  as  precipitation 
does  not  produce  pseudo-adiabatic  conditions.  While  there 
is  rain  falling  from  the  cloud  at  some  distance  to  the  south, 
where  the  approximate  adiabatic  process  has  been  disturbed, 

£ 

it  yet  seems  proper  to  retain  the  full  ratio   „  =  0.0130   for 

computing  along  the  line  from  the  waterspout  to  the  apex  of 
the  cloud,  since  it  is  probable  that  the  activity  of  the  cloud 
continues  still  to  be  nearly  adiabatic  along  the  main  line  of 
ascension  of  the  vapor  of  condensation.  It  is  to  be  particu- 


also  the  same  ratio  -j-  must  be  kept,  so  that  there  remain  the 
n 

two  variables  B  and  t.  Now  the  connection  between  t  and  e  is 
fixed  at  a  certain  value  by  the  saturation  tables,  so  that  if  £,  is 
assumed,  e^  is  found  by  the  table,  and  B^  is  obtained  by  computing 
backwards  through  Tables  95,  96,  the  result  being  checked  by 


having  the  ratio    ]  =  0.0130. 
B. 


This  usually  requires    a   few 


trials  to  effect  correctly,  and  one  needs  a  little  practise  with 
the  data  to  do  it  expeditiously.  In  order  to  make  a  beginning 
with  the  trial  temperatures  it  is  well  to  remember  that  in 
dealing  with  cumulus  clouds  the  average  fall  in  temperature 
in  passing  from  the  sea  level  to  the  base  of  the  cloud,  through 
1100  meters,  is  usually  10°  to  11°  C.  This  is  shown  in  Table 

147,   where  for   the    surface  temperature   t  =  20°,   and  —  = 

B 

o 

0.0143,  which  is  the  original  value  of  --  ,  we  have  for  the  tem- 

Bi 

perature  gradient  per  1000  meters,  Gt  =  —  9.50.  This  table  is 
adapted  for  the  cumulus  cloud-base  at  the  height  of  1000  to 
1100  meters  as  it  stands,  without  modification.  If  the  tem- 
perature is  for  any  other  height,  the  gradient  must  be  modi- 
fied somewhat  as  indicated  by  the  subtable  on  page  727, 
though  the  gradients  may  become  very  abnormal  under  cer- 
tain conditions.  It  is  proper  from  these  considerations  to 
begin  the  trial  values  of  tv  the  temperature  at  the  base  of  the 
cloud,  with  tl  =  9°,  and  tt  =  10°.  These  values  will  give 


larly  noted  that  this  ratio,  ^  =  0.0130,  is  to  be  used  in  com-     resulting  values  of  the  -J-  which  will  enable  us  by  interpola- 


puting every  stage,  and  is  the  quantity  that  controls  the  value 
of  the  pressure,  temperature,  and  vapor  tension  at  all  the 
levels  of  the  cloud.  The  fact  that  the  heights  computed  by 
the  thermodynamic  processes  are  found  to  be  in  close  agree- 
ment with  those  measured  on  the  photograph,  according  to 
the  data  of  the  survey,  also  tends  to  justify  the  adoption  of 

o 

that  value  of  the  ratio  -. 

B 

The  constant  <?„  in  the  a-stage  is  computed  as  follows: 

/  e  \ 

Ia       1.3596     Table  95,  arguments  (  t  =  19.72,  B=  0.0130J. 

/  e  \ 

Ha  _    .4574     Table  96,  arguments  I  B=  763.3,  £=  0.0180  J. 

Ca       0.9022     Sum  of  Ia  and  IIa  =  constant. 

These  values  should  be  determined  with  accuracy  t&  the 
fourth  decimal  place  throughout  the  computation,  and  the 
result  will  then  be  sufficiently  exact  to  follow  the  natural 
processes  exactly  as  they  develop.  The  significance  of  the 
constant  Oa  =  0.9022  can  be  understood  from  this  considera- 
tion. We  have  a  set  of  mutually  related  thermodynamic  quan- 

tities, B  =  763.3,  t  =  19.72°,  e  =  10.92,  g  =  0.0130,  connected 

together  in  such  a  way  as  to  give  the  constant  0.9022. 

There  are  many  other  sets  of  values  of  B,  t,  e,  which  can  be 
developed  by  changing  the  thermodynamic  system  adiabati- 
cally,  that  is  to  say  without  adding  or  subtracting  any  heat. 
Now,  as  a  given  mass  of  the  aqueous  vapor,  so  many  grams 
per  thousand  grams  of  air,  or  so  many  thousandths  of  one 
kilogram,  rises  from  the  sea  level  and  ascends  upward  to  the 
base  of  the  cloud,  it  evidently  passes  through  pressures  and 
temperatures  which  are  each  diminishing  in  amount.  Then 
at  a  certain  height,  where  the  pressure  and  temperature  are 
sufficiently  reduced,  this  same  mass  of  vapor  will  begin  to 
saturate  the  kilogram,  and  condense  as  visible  vapor.  In  all 
the  steps  of  change  in  B,  t,  e  from  the  surface  to  the  cloud- 
base,  the  same  constant  <7a  =  0.9022  must  be  retained,  and 


tion  to  find  the  correct  value  of  tl  at  the  third  trial. 

The  following  form  illustrates  the  method  of  procedure  for 
-assumed  successive  values  of  tr     The  last  column  gives  the 
arguments,  or  the  method  of  obtaining  the  figures  in  the  second 
and  third  columns: 
<,         9°  10°  (Assumed.) 

el         8.55  9.14       Smithsonian  Table  43. 

I.        ,350,       i*.}**-*,     j{'  =  9°    J" 

arguments.       ]  ;  =  10°,  e  =  0.0130 
I  J    I  -B 

Ga        .9022         .9022     From  preceding  result,  formula  145. 


IL  —  .4485  —  .4493 


-  L  =11, 


B.  670  678    JTable96>    1.1=0.0130. 

(  argument,  j  B 

£L        0.0128       0.0135     Resulting  ratio  of  |L. 

-"l  •"! 

This  ratio  should  have  come  out  -J-  =  0.0130  if  the  trial  val- 
ues of  tl  had  been  correct,  and  interpolation  shows  that  in 
order  to  make  it  so  the  value  of  <,  should  be  9.3°. 

Repeat  the  computation, 
*,  9.3° 

e  8.72  Smithsonian  Table  43. 

Ia  .       1.3509       Cloud  Report  Table  95. 
(7a          .9022      As  above. 


(\  nisn 
M- 


!!„    -  .4487 

B1  672         Cloud  Report  Table  96. 

This  completes  the  check,  and  gives  £,=  672, 
<l=9.3°,e1=8.72  at  the  base  of  the  cloud. 

We  next  compute  the  height  at  which  the  visible  cloud  base 
floats  above  the  sea  level. 

For  Table  91  we  have  the  formula  of  barometric  reductions 
and  the  corresponding  height, 


365 


MONTHLY  WEATHEB  REVIEW. 


AUGUST,  1906 


log  Ba  —  log  J5,= 


7;  763.27 
7?,  672 


••  +m —  /3m — ym. 

Logarithm. 

2.88268 
2.82737 


m  —  /3m  —  fm,          .05531 

Since  Table  91  is  constructed  to  find  m  through  the  argu- 
ments, height  =  H  and  mean  temperature  Tm  =  0,  in  order  to 
obtain  H  by  the  inverse  process  we  must  compute  m  itself 
fromm  —  /3m  —  ym=.  05531,  by  taking  m  =.05531+  /3m  +  rm. 
By  Table  92,  with  the  arguments  (7?0=763  and  e0=10.9)  we  have: 


I=.378      = 


0054  and 


For  argument 

For  argument  II=/3  (for°assumed//=1100)  .0048 

So  that+/3m  (for  m=.055)  .......................  +0.00026 

By  Table  93,  +rm  (for  <o=41.5°)   .................  +0.00001 

Hence,  since  log  7?0—  log  7?,=  ......    .............     0.05531 

We  have,  m  ____  ."  ...............................     0.05558 

Finally  the  temperature  0=£  (19.7  +  9.3)  =14.5°. 

By  Table  91,  with  the  arguments  (0=14.5  and  m=0.05558) 

we  find  by  interpolating  Ha  =  j  Jjj™  peters. 

We  thus  find,  from  the  thermodynamic  computation,  that 
the  height  from  the  sea  level  to  the  plane  of  condensation  at 
the  base  of  the  cloud  is  3537  feet.  From  the  measurements 
on  fig.  27,  2d  A,  as  contained  on  page  311,  the  approximate 
height  is  60  mm.  or  3600  feet.  Considering  the  uncertainty 
in  determining  the  exact  plane  which  is  the  base  of  the  cloud 
sheet,  where  the  vortex  motion  becomes  asymptotic,  it  is 
evident  that  we  have  reached  a  satisfactory  agreement  re- 
garding the  height  by  two  independent  methods.  Further- 
more, this  check  is  a  good  evidence  that  the  fundamental  data 
in  these  computations  are  in  harmony  geometrically  and  ther- 
modynamically,  and  we  may,  therefore,  feel  confident  that  the 
other  deductions  depending  upon  them  are  substantially  cor- 
rect. 

The  gradients  per  100  meters  for  the  a-stage  are  now  easily 
obtained. 


-B 


3c. 


whence  770  = 
1078  meters. 


763.3;         ta        19.7          e0      10.92 
B\    672.0          «,          9.3          e,        8.72 
Bl— Ba—  91.3   <,— 10     —10.4  e,— e0    —2.20 
Divide  Bl— 7?0  etc.  by  10.78,  or  the  height  in  units  of  100  meters. 
(G.  B)0  —  8.46  (G.t)0  —  0.963  (G.e)0  —  0.204 . . By  observation. 
(G.  B)c  —  8.40  (G.t)0  —  0.950  (G.e)c  —  0.192 .  .  Table  147,  I,  II, 

III  Cloud  Beport. 

The  tabular  gradients  are  found  in  Table   147,  page   724, 
which  gives  the  gradients  that  prevail  for  average  conditions, 

by  using  the  arguments  (ta=  19-7  and  j.  =  0.0145  ].   The  agree- 

\  / 

ment  is  such  as  to  show  that  the  meteorological  conditions 
forming  the  waterspout  cloud  are  entirely  in  harmony  with 
those  which  are  found  to  prevail  under  similar  circumstances, 
when  thunderstorms  and  tornadoes  are  in  action.  If,  how- 
ever, we  compare  them  with  the  gradients  found  under  the 
normal  August  conditions  as  given  in  the  Barometry  Beport 
for  Nantucket,  we  have  the  following  data  taken  from  page  707 : 


Inch.  °  F. 

Bm     29.977  ta  67.7 

#,       26.470  «,  60.4 

Convert  these  into  metric  measures. 


Bm   761.35 

Bl     672.34 

B,-Bm  -89.01 


t 


°  C. 

19.83 
<,     15.78 
-<    -4.05 


Inch. 

ea  .571  \  English 
el  .445  )      measures. 

mm. 

14.50  )  Metric 
11.30  }     measures. 
-3.20 


Divide  Bt—Bm  etc.  by  10.78,  or  the  height  in  units  of  100  meters. 
(G.  B)a    -8.24     (G.  t)B   —0.375     (G.  e)B  —0.296 

The  discussion  of  these  gradients  will  be  resumed,  as  they 
are  important  in  the  theory  of  atmospheric  vortices. 

(B)  THE  /3-STAGE,  OH  SATURATED  PROCESS. 

The  computation  of  the  numerical  value  of  the  meterologi- 
cal  elements  (B\  t\  e1)  at  the  top  of  the  ,3-stage,  or  the  bottom 
of  the  f-stage  (7?0,  ta,  ec),  proceeds  as  follows: 
«,  9.3°  C.      | 

B,  672  mm.    v  Taken  from  the  top  of  the  «-stage. 

8.72mm.   ) 

0.0130          The  same  as  adopted  for  the  «-stage. 
663.28 

0.0132 

Arguments. 
Ip  +1.3747    Table  97  ^=9.3°,-|  =.0130  Y 

Up         -.4419    Table  98  /R_e -663.3, 4  =-0130  Y 

\  &  / 

IIIp        +   .0173    Table  99  (z=9.3°,  j^  =  .0132  Y 

»  11  / 

<7p  0.9501  Constant  for  the  /3-stage. 

At  the  top  of  the  ,3-stage  two  quantities  are  fixed,  namely, 
temperature  ^=0°  and  e1=4.57  mm.,  so  that  the  term  ~ 
be  at  once  found  and  subtracted  from  the  constant. 
tl  0° 

e1  4.57  mm. 


el 
e 
B 
B-e, 


B-et 


can 


.3664     Table  97,  arguments  U=0°,  |  =.0130  V 


1 
0.9501 


taken  from  above. 


—0.4163     Subtract  !„  from  £„. 

The  term  —0.4163  is  made  up  of  Up  and  ITl$  at  the  top  of 
the  /3-stage,  and  these  depend  upon  finding  by  trials  B1,  the 
pressure  there  prevailing.  It  is  convenient  to  employ  Hertz' 
well-known  diagram  of  adiabatic  changes  in  the  «  ft  •(  8  stages, 
a  copy  of  which  is  given  in  Professor  Abbe's  Translations, 
The  Mechanics  of  the  Earth's  Atmosphere,  page  202,  in  order 
to  have  approximate  values  to  figure  the  trial  computations. 
Enter  the /3-stage  at  the  point  7^=672,  <,=9.3°,  and  follow 
the  system  of  /3  lines  up  to  t  =  Q°  and  77=552.  Make  two 
trials  by  two  assumptions  of  the  pressure  B1. 
B1  552.0  542.0  Assumed  values  of  B1 

e1  4.57          4.57 

#i_ei     547.4         537.4 


.0084         .0085 
—.4289     —.4276 


+  .0115     +.0116 


Table  98,  arguments 
1— e'=547.4,  e-  =.0130 

537.4, 
Table  99,  arguments 


=  .0084 
=  .0085 


11+ III      —.4174     —.4160 

The  term  11+ III  should  be  equal  to  — .4163,  and  hence  we 
interpolate  another  assumed  value  of  7?l=544.  Bepeat  the 
trial, 


AUGUST,  1906. 
B 

e1 


MONTHLY  "WEATHER  REVIEW. 


366 


544         Assumed  by  interpolation. 
539.4 


B1 


HI 


.0085 

—.4279 
+  .0116 


Assume 


Arguments. 

Table  98,      (V-e'=  539.4  *=.013o) 
\  B  I 

Table  99,     (t  =  0, 


— e 


.0085^ 


11+  in—  .4163      The  check  is  complete  for  5'=  544. 

The  computation  for  Hp,  the  depth  of  the  /3-stage,  is  as  fol- 


• for  the  top  of  the  /--stage. 


Arguments. 

'— e°  =  534.4,    e=0.013oV 
a  J 

(t=0,  -JS-ji  =  .0086  V 

\ 


lows: 


Bt     672 
B1     544 

/3m 

Logarithms. 

2.82737 
2.73560 

n     0.09177 
+          38 
+            1 

<=9.3° 


e1==8.72 
el=4.57        «'= 


0=4.7C 


Table  92  T  I  =.0050, 
Table  93     e,=8.7 
|_5,= 


Arguments. 


11= .  00411 
H=  1700 
m=.092 


/  e  \ 

rVv    —.0024  Table  100U=0,  ^  =0.0130  1 

Sum  —  .4163     This  satisfies  the  check. 

For  the  depth  of  the  f-stage  we  compute, 

Logarithms. 

B0       544.    2.73560 
B°       539.    2.73159 


0.09216 

_  (  1728  meters.    Table  91,  arguments  (0=4.7°, m=. 09216). 
P"™1  {  5669  feet. 

The  gradients  for  the  /3-stage  are  now  found, 

I  mm  °  C.  mm. 

B1        544  t1      0  e>=4.57 

B         672  t.      9.3  e,=8.72 


m 


ff. 


Bl-B  —  128 


i_    _9.3 


1728  meters. 


e'-e,-4.15 


m — ^TO — ym  .00401     The  corrections  for   —  /3m  —  ym  can  be 

neglected. 

j    74  meters.  Table  91,  argument  (0=0°,  m=. 00401) 
' '  '  |  243  feet. 

The  pressure  gradient  in  the  ^-stage  is, 
(G.  B0)0  =  6.76     By  observation. 
(G.  B0)c  =  6.70     Table  147,  V,  of  the  Cloud  Report. 

(D)    THE  (5-8TAGE.  OR  FROZEN   PROCESS. 

The  5-stage  extends  to  the  visible  tops  of  the  clouds,  and 
we  may,  therefore,  take  such  a  temperature  as  will,  through 


B. 


.0130. 


Divide  Bl—Bl  etc.  by  17.28,  or  the  height  in  units  of  100  meters.  the  intermediate  computation,  produce  a  height  which  agrees 

(G.Bt)0— 7.40     (G.tjo— .538     (£.e,)0— .240     By  observation.  with  the  height  measured  on  the  photograph.     A  preliminary 

(G.BJc  —  7.40     (G.tjc—  .540     (G.e^)c—  .260     Table  147,  IV,  for  trial  of    — 11°C.  for  the  temperature  gives  a  height  that  is 

somewhat  lower  than  the  apex  of  the  cloud,  and  a  second  trial 
of  — 12°C.  seemed  to  be    about    right,  so  that  it  has    been 

In  order  to  compare  this  with  the  normal  conditions  of  the  adopted  for  the  numerical  example, 
atmosphere  in  August,  we   again  take  the   Nantucket  data,         For  the  constant  in  the  5-stage,  we  have, 

Barometry  Report,  page  707,  where  (B,  t,  e)  are  given  on  the  tn 

3500-foot  plane  and  the  10000-foot  plane.  Bl 

The  depth  of  the  o-stage  =  Ha  =  1078  meters  =  3537  feet.  en 

The  depth  of  the  /3-stage  =  Hp  =  1728  meters  =  5669  feet.  ^ 

Height  of  top  of  /3-stage 

above  sea  level   Hl       2806  meters  =  9206  feet.  -^ 

By  interpolation  to  the  given  heights,  1078  meters=3537 

feet  and  2806  meters=9206  feet,  we  obtain  in  metric  measures,  e 
from  page  707  of  the  Barometry  Report,  the  data. 

mm.  °C.  mm. 

B1      548.6  t1          9.22  e1       4.95 

B,      671.6  t,         15.72  e,     11.25 


0°C.  ) 

539.  v  brought  from  the  top  of  the  j'-stage. 
4.57  j 
534.4 


'— B,  —  123.0     tl—t,     —  6.50       e1— e,  —  6.30 


II, 


Assume  tn 


Divide  by  17.28,  the  height  of  the  /3-stage  in  units  of  100 
meters.  Ills 

(G.B^B—7.11    (G.t^B—.BlG    (G.e^B—  -364 

These  sets  of  gradients  for  the  /3-stage  will  also  require     ''-Constant 
further  discussion. 

(c)  THE  7--8TAGE,  OR  FREEZING  PROCESS. 

In  the  freezing  stage  there  is  no  change  in  the  temperature, 
which  is  £0=0°,  nor  in  the  vapor  tension,  which  is  e0=4.57  mm., 
and  we  have  only  to  compute  the  variation  in  the  pressure  B0. 
Constant  110  +  III0  —  .4163  ] 


.0086 

.0130 

Arguments. 

1.3664  TablelOl,  (<-0,-£— .0130 V. 

\          B  I 

-  .4273  Table    98,  (su—en  =  534.4,  e-  =.0130 V 

+   .0134  Table  102,  (t=0 ,     e"      =.0086). 
\  B\\~en  ' 


.9525 
— 12°  C. 


L 


o 
e 

B 


0° 
544. 
4.57 

0.0130 


e11    1.64  mm.  Table  103, 
Is 
Constant  .9525 


Argument. 
t=—  12°C. 


1.3556  Table  101,  (<=-12,-?  =.0130  \ 
\  R  I 


brought  from  the  /3-stage. 


—  .4031  This  is  the  constant  to  determine  Bu. 
Assume  Bn        415.0       419.0 
e11  1.6  1.6 

B"—en  413.4       417.4 


367 


MONTHLY  WEATHER  REVIEW. 


AUGUST,  1906 


e" 


Bu—e" 


.0040       .0040 


IIa  -.4098  -.4105 

+  .0066       .0066 


Table  98,  argument. 


Table  102,  arguments. 


-.4032    -.4039 

Interpolation  indicates  7/u=414.5. 
Assume  B11     414.5 

e"         1.64 
B»—e"     412.9 

.0040 


Arguments. 
IIS        -  .4097    Table    98/7?"—  e"=412.9,^=.0130j. 


+.0066    Table  102  <=-  12°, 


\ 


—  .4031    This  checks  the  constant  for  the  pres- 

sure 7?n=414.5  mm. 
The  depth  of  the  <J-stage  is  found  as  follows: 

Logarithms. 


Bn     539.0     2.73159 
B"    414.5     2.61752 

m — Pm—ym 


Arguments. 

.11407  (        I  =  .0033(e=4.57,  5=539). 
.00029  \       II  =  .0026  (assume  77=  2000). 
(     /9m  =  .  0026  x.  114=.  00029. 


0  —  - 


m 
0-12° 


.11436 
=  -6° 


Arguments. 

2062  meters.    Table  91  (0=  —6°,  m=.  11436). 
6765  feet 
The  gradients  in  the  5-stage  are  now  found: 

mm.  °C.  mm. 


B11 
B,. 


414.5 
539.0 


t" 
t,. 


—12.0 
00.0 


Hs  =2062  m. 


B11-  Bn  -124.5     tll—tu  -12.0     eu-en  -2.93 

Divide  Bn—  Bn  etc.  by  20.62,  or  the  height  in  units  of  100 
meters. 

(O.Bn)0—  6.04  (O.tn)0—.5S2  (O.  eu)0  —.142  By  observation. 
(G.  Bn)c  -  6.50  (G.  tu)0  -.550  (G.  en)0  -.140  Table  147;    VI, 

VII,  Cloud  Report. 

The  top  of  the  cloud  is  about  5000  meters  above  sea  level, 

so  that  in  Seption  VII,  Table  147,  for  #=5000  and  -^  =.  0130, 

we  find  the  vapor  tension  gradient  (G.  eu)c  =  — 0.140  per  100 
meters. 

Table  51,  summary  of  the  data  for  the  Cottage  City  water- 
spout, August  19, 1896,  contains  the  results  of  the  preceding 
computations  on  the  thermodynamic  conditions  prevailing  at 
that  time,  in  both  the  metric  and  the  English  systems  of 
measures.  The  first  column  of  figures  under  each  system 
gives  the  vertical  distances  H,  measured  in  millimeters  and 
inches  on  Hallet's  photograph,  2d  C,  taken  at  about  1:08  p.  m. ; 
the  second,  the  corresponding  height  in  meters  and  feet; 
the  third,  the  pressure  in  millimeters  and  inches;  the  fourth, 
the  temperature  in  degrees  centigrade  and  Fahrenheit;  the 
fifth,  the  vapor,  tension  in  millimeters  and  inches;  the  last 
column  the  gradients  as  extracted  from  the  Cloud  Report  from 
the  same  data;  also  the  gradients  as  deduced  from  the  Baro- 


metry  Report  for  the  same  season  of  the  year.     By  inspection, 
it  is  noted: 

(1)  In  the  a-stage  in  the  English  measures,  the  pressure 
gradient    has  increased  from  —0.098  to  —0.101  per  100  feet. 
The  normal   gradient  for  August  at  Nantucket,  only  a  few 
miles  from  the  scene  of  the  waterspout,  is  —0.098  per  100  feet, 
making  a  pressure  fall  of  — 3.47  inches  from  the  sea  level  to 
the  base  of  the  cloud,  or  a  change   of   pressure  from  30.05 
inches  to  26.58  inches;  the  waterspout  gradient  — 0.101  per 
100  feet  gives  a  fall  of  —3.58  inches  and  a  pressure  of  26.47 
inches  at  the  height  3537  feet,  the  base  of  the  cloud.     There 
is  thus  a  total  change  in  the  vertical  gradient  of  0.11  inch 
from  the  sea  level  to  the  cloud,  and  it  is  this  increased  differ- 
ence of  pressure  which  causes  the  air  to  rise  generally  from 
the  surface  of  the  sea  to  the  cloud,  and  is  intimately  concerned 
with  the  generation  of  the  vortex  tube.     We  may  remark  in 
passing  that  one  of  our  purposes  in  constructing  tables  and 
charts  of  the  normal  values  of  the  pressure,  temperature,  and 
vapor  tension  on  the  3500-foot  and  the  10,000-foot  planes,  in 
connection  with  their  values  on  the  sea-level  planes,  was  to 
afford  the  data  for  establishing  the  normal  vertical  gradient  in 
the  lower  strata  of  the  atmosphere,  which  shall  represent  the 
average    stratification    when    undisturbed    by    convectional 
action.     It  is  very  desirable  that  these  gradients  should   be 
checked  by  numerous  direct  observations  of  B,  t,  e,  taken  day 
and  night,  winter  and  summer,  so  that  the  normal   gradients 
can  be  separated  from  the  convectional  gradients  in  a  per- 
fectly reliable  manner.     As  this  must  be  the  work  of  years 
for  the  United  States,   it  is  permissible  to  employ  the  gra- 
dients contained  in  the  Barometry  Report,  which  rest  upon 
the  best  data  we  now  possess,  in  such  discussions  as  are  sug- 
gested by  the   Cottage  City  waterspout.     Similarly,  the  phe- 
nomena of  tornadoes  in  the  Mississippi  Valley,  of  thunder- 
storms   generally,  of  cyclones,  anticyclones,  and  hurricanes 
can   be  properly  studied   only  by  comparing   the   abnormal 
gradients,  prevailing  in  these  conditions  of  rapid  convection, 
with  these  normal  gradients.     The  differences  between  these 
two  systems  of  gradients   represent  the   energy  which   pro- 
duces these  atmospheric  motions,  and  any  explanation  of  the 
cause  of  the  change  of  the  gradients  from  the  normal  to  the  abnor- 
mal, or  convectional  types,  is  undoubtedly  a  direct  contribution 
to  the  scientific  theory  of  the  local  circulations  of   the  air. 
The  Barometry  Report  has  furnished  us  for  the  first  time  with 
the  data  for  constructing  the  isobars  on  the  higher  levels,  as 
is  shown  on  the  charts  published  in   the  MONTHLY  WEATHER 
REVIEW  for  January  and  February,  1903.     The  series  of  charts 
containing   the  daily  isobars  on  three  planes  lays  bare   the 
mechanism   of  the  dynamic  structure  in  cyclones  and  anti- 
cyclones, so  that  it  is  necessary  to  develop  a  mathematical 
analysis  in  conformity  with  the  observed  facts.     Furthermore, 
the  same  Barometry  Report  has  furnished  us  with  reliable 
annual  residuals,  or  the  variation  of  the  pressure  from  year  to 
year,  and  it  has  been  shown  in  the  MONTHLY  WEATHER  REVIEW 
for  July,  1902,*  that   these  residuals  synchronize  with   similar 
pressure  variations  over  the  entire  earth,  and  also  to  some 
extent  with  the  annual  variations  in  the  frequency  numbers  of 
the  solar  prominences,  faculae,  and  sunspots.     These  facts  sug- 
gest the  foundation  for  the  true  cosmical  meteorology  of  the 
future.     These  three  lines  of  study — namely,  (1)  the  abnormal 
system    of  convectional   gradients,  (2)  the  normal  gradients 
when  there  are  no  vertical  currents,  and  (3)  the  solar-terres- 
trial synchronous  variations — can  be  developed  with  accuracy 
for  the  United  States,  and  placed  upon  a  strictly  scientific 
basis.     Could  similar  material  be  computed  for  several  other 
parts  of  the  earth,  the  whole  cosmical  research  would  be  dis- 
tinctly advanced  from  an  empirical  to  a  thoroughly  scientific 
status.     The  point  of  view  can  be  illustrated  by  employing  the 
data  obtained  from  the  Cottage  City  waterspout,  Table  51. 
1  Vol.  XXX,  pp.  347-354. 


AUGUST,  1906. 


MONTHLY  WEATHEE  REVIEW. 

TABLE  51. — Summary  of  the  data  for  the  Cottage  City  waterspout,  August  19,  1896. 


368 


Metric  system. 

English  system. 

Stages. 

H.  photo. 

Height. 

B. 

(. 

e. 

II.  photo. 

Height. 

B. 

'     t. 

e. 

Gradient. 

mm. 

Meters. 

mm. 

°C. 

mm. 

Inches. 

feel. 

hit'tirx. 

°f. 

Inches. 

(-Upper.... 

176.4 

4942 

414.5 

-  12.0 

1.64 

6.95 

16,214 

16.32 

10.4 

0.065 

C 

radients 

C 

radients 

73.6 

2062 

J      -  6.  01 

\      -  6.  50 

-    .682 
-    .550 

-    .112 
-    .110 

2.90 

6,765 

>      -  .  072 
)      -  .  078 

-  .319 
-  .302 

-  .  00170 
-  .  00169 

(G)  Observed, 
(G)  Cloud. 

I 

[Lower  

102.8 

2880 

539.0 

0 

4.57 

4.05 

9,449 

21.22 

32.0 

0.180 

•I  6 

74 

—  6.76 

0.10 

243 

—  .082 

(G)  Observed. 

Upper  .... 

100.2 

2806 

544.  0                      0                 4.  57 

3.95 

9,206 

21.42 

32.0 

0.1HO 

Gradients. 

C 

radients 

C      -7.10 

—    .638        -    .210 

C      -  .089 

-  .291 

-  .00288     (G)  Observed. 

/3-stage  Range  .... 

61.7 

1728 

<     -  7.60 
\     -7.11 

-    .610         -    .260 
-    .376        -    .361 

2.43 

5,669 

]     -  .  091 
(     -  .  086 

-  .294 
-  .207 

—  .00312 
-  .  00137 

(G)  Cloud. 
(G)  Barometry. 

[Lower  

38.5 

1078 

672.0 

9.  3               8.  72 

1,52 

3,537 

26.46 

48.7 

0.343 

f  Upper.... 
a-stage                 -[Range.... 

38.5 

C 
(      -  8.  16 

1078   \      -  8.  10 

(  -  s.  21 

rradients 
-  0.  963 

-  0.950 
-  0.376 

-0.201 
-  0.192 
-  0.296 

1.52 

3,537 

r 

C    -  0.101 

I  -  0.101 

<    -  0.  098 

radients 
-  0.  531 
-  0.  522 
-  0.  206 

'  -  0.  00216 
-  0.  00230 
-  0.  00355 

(G)  Observed. 
(G)  Cloud. 
(G)  Barometry. 

I  Sea  level.. 

0 

0           763.27 

19.72 

10.92 

0 

0 

30.05 

67.5 

0.430 

(2)  In  the  temperature  of  the  a-stage  the  normal  gradient  is 
—0.206  F.  per  100  feet,  and  the  waterspout  gradient  is  — 0.531, 
which  is  only  a  little  short   of  the  true  adiabatic    gradient. 
The  normal  temperature  fall  from  the  sea  level  is  — 7.3°,  or  a 
change   from   67.5°    to    60.2°,   at   the  3537-foot  level.     This 
change  from  the  normal  temperature  fall  (which  is  small  on 
the  Atlantic  coast  in  summer  because  of  the  southward  bend- 
ing of  the  isotherms  over  the  ocean   areas)  to   the   adiabatic 
convectional  gradient  is  a  very  striking  fact.     The  latter  gives 
a  fall  of  —18.8°  F.,  or  a  fall  from  67.5°  to  48.7°  F.,  instead  of 
to  the  normal  temperature  60.2°  F.,  showing  that  something  has 
occurred  to  suddenly  reduce  the  normal  temperature  at  the  3637- 
foot  level  by  the  amount  11.5°  F. 

The  cause  of  this  will  be  explained  in  the  following  para- 
graph. 

(3)  The  normal  gradient  of  the  vapor  pressure  is  —0.00355 
inch  per  100  feet,  for  Nantucket  in  August,  and  this  gives  a 
total  fall  of  — 0.126  inch,  or  a  change  from  0.430  at  sea  level 
to  0.304  at  the  cloud  base.     The  abnormal  or  convectional  gra- 
dient prevailing  at  the  waterspout  is  0.00246,  which  makes  a 
change  of  — 0.087,  or  a  diminution  of  the  normal  vapor  pres- 
sure 0.430  to  0.343.     Thus,  we  have  a  gain    of  0.039  in   the 
vapor  tension  for  the  waterspout.     The  result  for  the  a-stage 
is  a  total  decrease  of  the  pressure  by  — 0.110  inch,  a  total  de- 
crease in  the  temperature  by  11.5°  and  a  total  increase  in  the 
vapor  tension   by  0.039   inch.     This  must  be  interpreted  to 
mean  that  the  air  is  rising  from  the  sea  level,  carrying  with  it 
aqueous  vapor  into   levels  of   temperature    about  — 11.5°  F. 
lower  than  that  which  prevails  in  the  normal  August  weather. 

(4)  The  depth  of  the  a-stage  is  3537    feet,  of  the  /3-stage 
5669  feet,  of  the  ^-stage  243  feet,  and  of  the  3-stage  6765  feet, 
to  the  assumed  top    of   the    cumulo-nimbus    cloud.     In   the 
,3-stage  the  pressure  gradient  changes  from  the  normal  rate 
—0.085,  to  the  convection  rate  —0.089  per  100  feet.     This  is 
equivalent  to  a  fall  of  — 4.82  inches  in  the  normal  state,  from 
26.58  to  21.76  inches;  and  to  a  fall  of  — 5.04  in  the  convection 
cloud,  from  26.46  to  21.42  inches.     There  is,  therefore,  a  total 
fall   in  pressure    of  —0.227    inch,   (—  .004  x  56.7  =  —  0.227), 
induced  by  the    change  from   the  normal  to  the  waterspout 
conditions  in  the  /3-stage  of  the  cloud.     We  have  thus  a  dif- 
ferential gradient  per  100  feet  in  the  a-stage  of  — 0.0031,  and 
in  the  /3-stage  of  — 0.0041  inch  in  favor  of  a  vertical  current. 
The  excess  in  the  /3-stage  over  the  a-stage  of  —0.0010  inch 
may  be  taken  as  the  effective  gradient  due  to  the  additional 
latent   heat   produced   by  the    condensation  of  the  aqueous 
vapor  to  liquid  water.      This  is  only  one-third  the  amount  of  the 


gradient  due  to  the  cause  which  produces  the  general  uplift  of  the 
air  that  feeds  the  cloud.  This  criterion  also  proves  that  there 
is  a  more  efficient  cause  for  the  vertical  pressure  gradient  than 
the  condensation  of  the  aqueous  vapor,  which  has  been  so 
generally  considered  by  meteorologists  to  be  the  true  source 
of  the  energy  that  drives  cyclones,  following  Espy's  sugges- 
tion of  fifty  years  ago. 

(5)  The  temperature  gradient  in  the  /S-stage  changes,  de- 
rived for  the  normal,  is  -0.207°  F.  per  100  feet,  and  —0.294°  F. 
per  100  feet  in  the  cloud.     This  amounts  to  a  fall  of  .-11.7°  F. 
in  5667  for  the  normal  state,  and  — 16.7°  F.  for  the  convec- 
tional state,  carrying  the  normal  temperature  from  60.2°  to 
48.5°  F.  in  the  /3-stratum,  and  from  48.7°  to  32.0°  F.  in  the 
actual  /3-stage  of  the  waterspout  cloud.     This  is  equivalent  to 
a  gradient  excess  in  the  a-stage  of  — 0.325  of  the  convection 
over  the  normal  gradient,  and  in  the  /3-stage  is  one-fourth 
that  in  the  a-stage.     In  the  case  of  the  pressure  the  excess  in 
the  /?-stage  is  four-thirds  that  in  the  a-stage.     The  tempera- 
ture difference  of  gradient  diminishes  rapidly  in  proportion 
to  the  height  up  to  the  f-stage.     In  that  stage  and  the  3-stage 
there  is  not  much  difference  between  the  normal  and  the  com- 
puted convectional  gradients.     This  indicates  that  the  effec- 
tive cause  of  a  vertical  gradient  is  about   exhausted  at  the 
height  where  the  isotherms  of  the  0°  is  located,  or,  in  other 
words  that  the  vertical  convectional  action  is  properly  confined  in 
the  waterspout  cloud  to  within  about  two  miles  of  the  ground,  and 
is  most  active  in  the  lower  portion  of  the  cloud.     In  cyclones  this 
vertical  convection  is  usually  limited  to  within  two  or  three 
miles  of  the  ground,  though  the  accompanying  dynamic  action 
may  penetrate  into  the  upper  strata  as  high  as  three  or  four 
miles;  in  hurricanes  the  penetration  reaches  to  six  or  seven 
miles  at  least. 

(6)  In  the  /9-stage  the  gradient  of  the  vapor  tension  changes 
from  the  normal  —0.00437  per  100  feet  to  —0.00288;  the  total 
fall  in  5669  feet  amounts  to  —0.248  inch,  ( —0.00437  x  56.7  = 
—0.248),  in  the  normal,  to  —0.163  in  the  cloud  convection, 
making  the  fall  which  should  be  from  0.304  to  0.056  in  the 
normal  state,  from  0.343  to  0.180  in  the  cloud.     The  differ- 
ence of  gradient  is  +0.00109  per  100  feet  in  the  a-stage,  and 
+  0.00149  in  the   /3-stage,  showing   that  large  quantities  of 
vapor  are  carried  upward  from  the  sea  level  in  both  stages,  but 
that  there  is  a  condensation  of  aqueous  vapor  to  water  equiva- 
lent to  -f- 0.00040  inch  per  100  feet.     We  can  not  carry  out  this 
comparison  between  the  normal    and  the    convectional    gra- 
dients in  the  ^--stage  and  the  3-stage,  but  the  evidence  is  that 
they  have  become  practically  identical. 


369 


MONTHLY  WEATHER  REVIEW. 


AUGUST,  1906 


(7)  It  is  desirable  to  compare  these  vertical  gradients  with 
the  commonly  observed  horizontal  gradients.  We  have  in 
the  pressure  — 0.34  inch  in  9206  feet.  This  is  equivalent  to 

—  13.47  inches  in  364,525  feet,  or  111,111  meters,  or  one  de- 
gree in  the  standard  latitude  of  forty-five  degrees.     Now,  on 
the  weather  maps,  — 0.70  inch  in  five  degrees,  or  — 0.14  inch 
in  one  degree,  is  the  average  horizontal  gradient  in  a  highly 
developed  cyclone.     Hence,  in  the  convectional  cloud  forma- 
tion the  vertical  gradient  is  about  one  hundred  times  as  large 
as  in  such  horizontal  motions.     In  the  temperature  the  fall  of 

—  16.5°  in  9206  feet  is  equivalent  to  —654°  in  111,111  meters, 
or  one  degree,  and  this  too  is  about  one  hundred  times  the 
horizontal  gradients  which  are  found  on  the  weather  maps. 
This  indicates  that  the  scale  of  operations  on  the  horizontal  plane 
is  only  one  hundredth  that  which  occurs  in  the  vertical  direction  in 
convectional  clouds.     The    linear    dimensions   of  cyclones  are 
usually  about  one  hundred  on  the  horizontal  to  one  in  the 
vertical  direction,  and  these  two  facts,  taken  together,  show 
how  much  less  force  is  required  to  drive  a  horizontal  than  a 
vertical  current. 

THE  CAUSE  OF    THE   FORMATION   OF  THE  WATERSPOUT    CLOUD,  AND    THE 
VERTICAL  CONVECTIONAL  VELOCITY. 

(1)  Vertical  convection  due  to  surface  heating. — We  now  reach 
the  important  question,  what  was  the  physical  cause  of  the 
formation  of  the  cloud,  and  the  vertical  convection  within  it 
that  was  the  immediate  condition  of  the  generation  of  the 
vortex  tube  extending  from  the  base  to  the  ocean?  Fortun- 
ately, one  answer  to  this  question  is  entirely  excluded  from 
our  consideration.  The  disturbance  of  the  normal  stratifica- 
tion which  produces  an  abnormal  system  of  gradients  and  the 
corresponding  vertical  currents,  may  be  due  to  two  causes, 
(1)  the  surface  layers  may  be  overheated  relatively  to  the 
upper  layers,  or  (2)  the  upper  layers  may  be  undercooled  re- 
latively to  the  surface  layers.  Either  cause  would  be  equally 
efficient,  and  it  is  only  a  question  of  which  one  is  actually 
operating  in  the  case  of  this  waterspout.  Overheating  the 
surface  layers  is  due  to  a  perfectly  definite  physical  process, 
namely,  as  follows.  The  effective  solar  radiation  falling  upon 
the  earth's  atmosphere  consists  of  short  wave  lengths  from 
0.30  fi  to  2.00/i.  (Compare  figs.  3  and  4,  Tables  1  and  2  of  my 
paper  on  "  Solar  and  terrestrial  physical  processes,"  MONTHLY 
WEATHER  REVIEW,  December,  1902,  Vol.  XXX,  pp.  562-564.) 
These  short  waves,  whatever  may  be  the  true  effective  solar 
temperature  at  which  they  are  produced,  penetrate  to  the  sur- 
face of  the  earth  with  two  sources  of  depletion,  the  first,  by 
scattering  in  the  upper  atmosphere  which  cuts  out  a  large 
percentage  of  them,  and  produces  the  strong  glare  that  is 
characteristic  of  the  higher  layers;  the  second,  by  absorption 
in  the  aqueous  vapor  at  certain  wave  lengths,  which  causes 
the  observed  depressions  or  cold  bands  in  the  energy  spec- 
trum. There  is  good  reason  for  believing  that  the  upper  as 
well  as  the  lower  atmosphere  is  heated  by  the  passage  of  the 
remainder  of  the  short  waves  by  only  a  very  slight  amount, 
and  that  this  is  practically  negligible  in  general  discussions. 
But  these  short  rays  falling  upon  the  surface  of  the  earth 
are  readily  absorbed,  and  this  absorption  powerfully  raises  the 
temperature  of  the  land  and  ocean  areas.  That  practically 
ends  the  history  of  the  incoming  solar  radiation. 

The  terrestrial  radiation,  on  the  other  hand,  is  of  an  entirely 
different  character,  and  it  has  a  very  different  effect  upon  the 
earth's  atmosphere.  The  heat  radiations  at  terrestrial  tem- 
peratures, where  the  absolute  temperature  ranges  from 
r=200°  to  T=3250,  have  wave  lengths  extending  from  %L  to 
40/i,  and,  thus  the  outgoing  wave  lengths  begin  where  the  in- 
coming lengths  end.  Many  of  these  long  waves,  in  radiating 
from  the  surface  of  the  earth,  are  quite  readily  absorbed  by  the 
atmosphere,  and  the  heat  percolates  from  the  lower  through  the 
upper  strata  by  a  process  of  slow  conduction  and  convection. 


The  aqueous  vapor  certainly  absorbs  many  waves,  as  from  4/j 
to  8,'t,  and  possibly  most  of  the  waves  beyond  12/j..  It  was 
shown  very  distinctly  in  my  International  Cloud  Report  that 
the  surface  temperatures  do  not  diminish  with  the  height  at 
an  adiabatic  rate,  but  much  more  slowly,  as  is  indicated  on 
charts  78  and  79.  In  Table  162  of  the  same  report  is  given 
the  number  of  calories  per  kilogram  required  to  convert  an 
adiabatic  atmosphere  into  the  actual  atmosphere  as  observed. 
It  shows  an  increase  from  the  ground  until  the  number  is 
about  9.5  calories  at  the  13,000-meter  level  in  summer  and 
11.0  calories  in  winter.  This  amount  of  heat  may  be  taken 
to  represent  the  effect  of  the  outward  flowing  flux,  which,  like 
a  slow  conduction,  keeps  the  upper  atmosphere  warmer  than 
it  would  be  if  the  outward-going  waves  had  the  same  length 
as  the  inward-coming  waves.  This  difference  in  wave  length 
is  the  most  important  factor  in  the  economy  of  the  earth's 
atmospheric  temperatures. 

We  may  now  fix  our  attention  more  closely  upon  the  changes 
in  the  surface  temperatures  as  measured  in  the  normal  diurnal 
and  annual  periods,  and  in  the  local  variations  of  all  kinds  upon 
the  average  conditions.  The  change  in  the  transparency  of  the 
atmosphere  due  to  cloudiness,  the  difference  of  altitude  of  the 
sun,  the  character  of  the  surface,  whether  water  area,  moist 
ground,  or  dry  desert,  all  determine  the  effective  temperature 
of  the  surface  at  any  given  time.  These  react  upon  the  cor- 
responding outgoing  radiation,  which  first  heats  up  the  lowest 
strata  of  the  atmosphere,  or  cools  it,  according  to  the  pre- 
vailing conditions.  Strong  surface  heating  by  day  and  cool- 
ing by  night  is,  therefore,  the  regimen  to  which  these  layers 
are  subject,  and  the  integral  effect  of  this  action  in  its  pas- 
sage through  the  upper  layers,  finally  builds  up  the  observed 
normal  gradients  of  temperature  which  by  no  means  produce 
an  abiabatic  rate  of  stratification.  Temporary  convectional 
currents  upward  by  day,  downward  by  night,  upward  in  some 
local  areas,  downward  in  other  areas,  constitute  the  common 
types  of  motion  due  to  these  causes.  The  formation  of  the 
lower  cumulus  clouds  with  moderate  convection,  of  thunder- 
storms in  strong  convection,  and  of  desert  sand  vortices  are 
typical  examples  of  purely  surface  overheating  with  vertical 
convection.  But  there  is  an  entirely  different  class  of  vertical 
convection,  to  which  sufficient  attention  has  not  been  paid 
in  meteorological  investigations. 

(2)  Vertical  convection  due  to  the  overflow  of  cold  upon  warm  cur- 
rents of  air. — It  is  evident  that  the  vertical  convection  in  the 
cumulo-nimbus  cloud  of  the  Cottage  City  waterspout  could  by 
no  possibility  have  been  due  to  the  overheating  of  the  surface 
by  the  incoming  solar  radiation.  The  phenomenon  occurred 
over  the  ocean  and  all  the  meteorological  data  of  Table  50  show 
that  there  was  actually  no  superheating  effect  near  the  surface 
at  that  time.  The  prevailing  temperature  was  67.5°  F.,  while 
the  normal  for  the  month  of  August  at  Nantucket  was  67.7° 
F. ;  and  the  humidity  was  64  per  cent,  while  the  normal  was  84.3 
per  cent.  In  fact,  the  19th  of  August,  1896,  was  the  driest  day  of 
the  entire  month,  and  the  powerful  vertical  convection  then 
taking  place  could  not  have  been  due  to  the  solar  radiation  act- 
ing on  the  surface  conditions.  We  must,  therefore,  look  for 
another  efficient  principle  capable  of  producing  the  powerful 
effects  shown  in  the  showers  preceding  the  family  of  water- 
spouts and  the  thunderstorm  with  downfall  of  hail  following 
them.  This  we  can  readily  discover  by  referring  to  the  weather 
chart  of  the  date,  August  19,  1896,  tig.  37. 

This  map  shows  that  a  well-defined  area  of  high  pressure 
was  just  pushing  its  southeastern  front  over  Vineyard  Sound, 
that  the  winds  were  from  the  northwest,  and  that  there  was  a 
fall  in  temperature  of  about  15°  along  the  coast  line,  due  to 
the  advance  of  this  cold  area.  We  have,  therefore,  merely  to 
assume,  in  accordance  with  the  general  fact,  that  the  upper 
strata  are  moving  eastward  in  advance  of  the  lower,  and  that 
this  cold  air  from  the  high  area  was  blown  forward  over  Vine- 


AUGUST,  1906. 


MONTHLY  WEATHER  REVIEW. 


370 


yard  Sound  earlier  in  the  strata  a  mile  or  two  high  than  at 
the  surface. 

A  sheet  of  cold  air  overran  the  low,  warm,  and  quiet  strata  about 
midday,  while  the  cold  air  followed  at  the  surface  a  few  hours  later, 
and  in  these  facts  we  have  the  exact  conditions  required  to  produce 
the  observed  powerful  convection.  Such  abnormal  cooling  of  the 
higher  strata  is  as  efficient  in  producing  vertical  convectional 
gradients  as  a  superheating  of  the  surface  would  be,  and  the 
evidence  that  this  was  the  actual  case  is  so  good  as  to  render 
it  a  practical  proof  of  this  circumstance.  The  upper  strata 
were  cooled  suddenly  by  — 12°  to  — 15°  F.,  and  this  brought 
showers,  the  waterspouts,  and  the  thunderstorms  in  close  suc- 
cession. These  were  followed  later  by  cooler  conditions  at 
the  surface,  giving  a  temperature  fall  from  the  maximum  of 
the  day,  72°,  to  the  minimum,  56.5°,  at  Vineyard  Haven.  Under 
these  conditions  all  the  observed  facts  find  so  natural  and 
satisfactory  an  explanation  that  no  further  remarks  seem  to 
be  needed  to  enforce  the  theory. 

But,  it  should  be  noted  that  this  overflow  of  relatively  cold 
layers  of  air  at  a  moderate  elevation  upon  the  warm  surface 
layers,  this  forereaching  and  temporary  stratification  causes  an 
abnormal  system  of  gradients  which  produce  the  vertical  cur- 
rents required  to  set  up  the  motions  that  tend  to  reestablish 
the  normal  equilibrium  of  the  atmosphere.  This  local  disturb- 
ance of  the  average  gradients,  due  to  the  fact  that  the  cold 
upper  air,  under  certain  configurations  of  the  lower  currents, 
is  drifted  forward  upon  them,  is  the  primary  cause  of  most  of 
the  phenomena  classified  as  thunderstorms,  tornadoes,  cyclones,  and 
hurricanes.  In  short,  all  these  violent  local  disturbances  of 
the  lower  air  are  largely  due  to  this  cause,  and  this  is  the  true 
source  of  the  energy  expended,  though  it  has  been  attributed  by 
one  school  of  meterologists  to  the  latent  heat  of  condensation, 
and  by  the  other  school  to  the  eddies  established  by  differen- 
tial horizontal  velocities.  These  two  latter  sources  of  energy 
need  not  be  excluded  from  consideration,  for  they  contribute 
their  quota  to  the  total  energy  of  circulation,  but  the  first 
cause  is  the  abnormal  stratification  of  the  air  at  moderate 
elevations.  Thus  the  groups  of  thunderstorms  which  frequent 
the  southeastern  quadrants  of  the  cyclone  are  due  to  the  over- 
flowing of  the  cold  northern  current  upon  the  warm  current 
from  the  south.  Tornadoes  have  the  same  origin  and  their 
location  shows  that  they  are  due  to  this  cause.  The  cyclone 
itself  is  generated  by  warm  currents  of  air  from  the  Tropics 


underrunning  the  cold  sheet  which  rotates  above  the  surface 
of  the  earth,  in  the  hemispherical  whirl  north  of  latitude  35°. 

The  reason  for  the  outflow  of  warm  currents  from  the 
Tropics  has  been  indicated  in  the  International  Cloud  Report, 
chapters  8  and  10;  also  there  will  be  found  in  the  MONTHLY 
WEATHEB  REVIEW  for  January  and  February,  1903,  and  in  the 
preceding  papers  of  this  series,  further  illustrations  and  re- 
marks on  this  theory.  The  West  Indian  hurricanes  in  a  simi- 
lar way  are  produced  in  the  late  summer  and  autumn  by  the 
overflow  of  the  cool  upper  sheet  from  the  North  American 
Continent  upon  the  warm  tropical  lower  strata,  because  this 
sheet  is  then  increasing  in  size  with  the  southward  retreat  of 
the  sun.  The  withdrawal  of  the  sun  to  the  south  in  fact 
brings  the  thermal  equator  of  the  higher  strata  toward  the 
geographical  equator  earlier  than  that  corresponding  to  the 
lower  strata.  Hence,  relatively  cold  air  from  the  temperate 
zones  at  considerable  heights,  begins  to  overlay  the  tropical 
warm  and  moist  lower  strata,  and  this  induces  the  long 
continued  vertical  convection,  localized  in  the  hurricane  vor- 
tex, which  in  its  progressive  movement  may  traverse  thou- 
sands of  miles  along  its  parabolic  track.  The  form  of  the 
track  is  due  to  the  influence  of  the  general  circulation  local- 
ized in  centers  of  action,  which  builds  the  south  Atlantic 
high  area  on  the  ocean  and  is  manifested  in  the  trade  winds, 
so  that  the  hurricanes  usually  gyrate  along  the  edge  of  this 
special  configuration. 

The  power  which  is  expended  for  days  in  succession  in  a 
hurricane  is  due  to  the  fact  that  the  wide  expanse  of  the  upper 
cold  sheet  covers  the  temperate  zones  and  overlaps  the  Tropics 
at  moderate  heights.  As  long  as  this  contrast  of  temperature, 
due  to  abnormal  stratification,  continues,  there  is  a  sufficient 
source  of  energy  in  the  resulting  thermal  engine  to  produce 
powerful  vertical  convection  currents,  and  to  sustain  the 
most  violent  hurricanes,  in  which  the  vortex  has  a  depth  of 
several  miles  in  a  vertical  direction.  This  theory  seems  to 
harmonize  completely  with  what  is  known  about  the  meteor- 
ology of  the  lower  air,  and  to  be  such  a  satisfactory  escape 
from  the  difficulties  of  (1)  the  condensation  theory  and  (2)  the 
dynamic  eddy  theory,  which  have  always  encountered  both 
practical  and  theoretical  objections,  that  we  may  expect  to 
find  confirmation  of  it  in  the  future  development  of  the 
mechanics  of  the  atmosphere. 


OCTOBER,  1906. 


MONTHLY  WEATHER  REVIEW. 


470 


STUDIES  ON  THE  THERMODYNAMICS  OF  THE  ATMOS- 
PHERE. 

liy  I'rof.  FRANK  II.  HIGEI.OW. 

VIII.— THE  METEOROLOGICAL  CONDITIONS  ASSOCIATED  WITH 
THE  COTTAGE  CITY  WATERSPOUT— Continued. 

RELATIONS  BETWEEN   WIND  VELOCITIES  AND  ATMOSPHEKIC  PRESSURES. 

In  meteorology  there  are  various  relations  depending  on 
the  influence  of  wind  velocities  upon  pressure,  which  must  be 
considered  in  addition  to  the  usual  static  barometric  pressure 
used  in  the  construction  of  synoptic  weather  maps,  and  in  the 
determination  of  heights.  Those  reductions  assume  that  the 
air  is  calm,  and  that  the  difference  of  pressure  depending  on 
wind  velocity  may  be  neglected.  On  the  other  hand,  in  torna- 
does, waterspouts,  hurricanes,  and  strongly  developed  cyclones 
the  velocity  of  the  wind  gives  rise  to  variations  of  pressure 
from  point  to  point.  In  theoretical  meteorology,  and  in  the 


practical  calculation  of  the  effects  of  high  winds  upon  build- 
ings and  other  structures,  as  when  a  tornado  passes  over  a  city 
or  thru  a  forest,  it  is  very  important  to  have  a  definite  knowl- 
edge of  the  relations  between  these  two  phenomena.  The 
literature  of  this  subject  is  very  extensive,  but  an  attempt  will 
be  made  to  bring  together  in  suitable  form  for  reference  the 
facts  likely  to  be  of  value  to  meteorologists,  engineers,  and 
architects. 

FORMULAS    FOE    WIND    VELOCITIES    AND    PRESSURE    GRADIENTS. 

Table  52,  formulas  1-13,  contains  the  development  of  the 
velocity-pressure  function  from  the  primary  equation  (203), 
page  505,  Cloud  Report,  Vol.  II,  1898-1899.  By  means  of  the 
auxiliaries  on  the  side  of  the  table  the  final  equation  13  is 
found, 


TABLE  52. — Formulas  for  wind  velocities  and  pressure  gradients. 


Auxiliaries. 


(1) 
(2) 

(3) 
(4) 

(5) 

(6) 

(7) 


OP 


=      i  u  +  vO  v  +  wdw  -f-  gdz. 

0  P  P  T 

—       °       =  udu  +  vdv  +  wdw  -\-  gdz. 

2'    /'o  T* 

P   =  -  p  =  P\\ 
1    Tn 


P         Po 


P  Tn 


gdz). 


i  T  r  i 

-logp=  —  j  T°      5  (52-?o2)  +  0  (z-<0 

logn  Po-log,,  p  = 
log  p-log  p  = 


-l^  9 


dP  _dp  _9B 

~r^==Y~~  :~~B" 

/)m=  13595.8  kilograms. 
/>„  =  1.29305  kilograms. 
I  =  7991.04  meters. 
g0  =  9.806      meters. 

Natural  logarithms. 
Common  logarithms. 


J  B  =  0.001742  B  ql. 


Integrate  the  velocity  term  alone  when  the  gravity  term  is  omitted. 


(8) 

(9) 

(10) 

(11) 
(12) 
(13) 

(14)  Standard. 

(15)  Other  density. 


=  0.001742. 


q  2=  574.06 
q  =  23.06 


29,1 

For9o  =  0. 


B  and  AB  in  meters. 

q  =  velocity  in  meters  per  second. 


TABLE  53. — Barometric  gradient  sustaining  an  eastward  velocity  only. 

Auxiliaries. 

D=  111  111  000  in  millimeters. 
;/„=  9.806    meters. 

2  n  =  0.000  1458. 

5=0.1572   "    f^usiny.  „  .        „,. 

760    T  l>  m  millimeters. 

17?  7? 

=  .._  _0      -v  sin  <f= 0.05646    -  usin  y>.  v  in  meters  per  second. 

17.7.J  ±  ./ 


AR=  In  v  sin  <f  =  0.1572  usiny. 

10514.5  g 


471  MONTHLY  WEATHER  REVIEW.  OCTOBER,  1906 

TABLE  54. —  The  Newtonian  theorem. 


(1)  --  . 

P  1  =9P- 

(10)  -  <jdp 


Auxiliaries. 
Takeu=«=0. 


(17)  -dp=  P  wdw  +  pgdh.  By  integration. 


(19)  -p  =  pZgv?  +  Ph, 

(20)  w'=  2gh.  Law  of  a  freely  falling  body  for  p=0. 

it? 

(21)  Py=  P  o~  ^-  Newtonian  theorem.     For  area  A. 

TABLE  55.—  The  vertical  velocity  that  just  sustains  a  freely  fatting  body. 
Units.     Meter-kilogram-second.     (M.  K.  S.) 

*      B     a  Notation. 


(22)  General  formula.  A  B  = 


(23)  Pressure  A  pA=  A  B  am  A  =  -=7  Wfi    ™  v?  A 


574.06  T  w  jn  meters  per  second. 

13595.8  B  kilogram  A  =  surface. 


=7      fi    ™  - 

574.06    T  m*  a  =  1000  p  kilograms. 

,,,=  135958. 
r,  D  in  meters. 
B,  A  R  in  meters. 


=  23.68*^.  ,,,,=  135958. 

T  r,  D  in  meters. 


=  0.08675  B  ±4  vf  A. 
=  0.065936  -g-  y? 

0 

i          i    jy 

The  equivalent  normal  surface  for  a  sphere  =  A  =      ^  rt  =      ,  The  velocity  must  be  increased  by  some  factor  k,  as 

u  SB       4 

determined  by  experiments,  to  allow  for  the  action  of  the  body  in  modifying  the  stream  lines  of  pressure.     Ferrel   assumes 
k  =  1.104;    Schreiber,  k  =  1.3. 

(fe=1.00)  Ferrel(/c=  1.104)  Schreiber  (fc=  1.30) 

(24)  Pressure  ApA  =  A  B  am  \  nr*  =  37.200  B  r'u?  k.  41.07  48.36 

L  J. 

=  9.300  B  D'w'k.  10.27         12.09 

=  0.10356  ^-  T*  r'vfk.  0.11436       0.13464 

JL>n      J. 

=  0.02589  B    T°D*iu1lc.  0.02859  0.03366 

The  weight  of  the  body  to  be  just  sustained,  a  =  specific  weight. 

(25)  Weight  Wa  =  f-  *  »•'  P  x  1000  kilograms  =  4188.8  r3  p  =  4188.8  r"  ^ 

/'l 

=  *  ff  ^  ^  x  1000  kilograms  =    523.6  Z*3  /.  =  523.6  Z)8  ?J? 
"8  ^) 

(26)  Specific  weight  ?•  =  specific  weight  of  body  = 

/Oj      specific  weight  of  water 

,„_,  p       density  of  air  above  surface       B    T0 

/>„  ~       density  of  air  at  surface       ~  B0  T' 

(28)  For  equilibrium  J  pA  =  Wg  =  37.200         E-    r1.  w>.  k  =  4188. 8  r'.   Pv>. 

(29)  =     9.300         BT    D\ii?.k=    523.6  Z>'./<,,, 

(30)  =  0.10356  ^»  ^  r1.  w>.k=  4188.8  r8.  />,„. 

(31)  =  0.02589  ^-  ^  Z>'.  w'.  k  =  523.6  Z>".  Pw. 


OCTOBER,  1906. 

(32) 
(33) 
(34) 
(35) 


MONTHLY  WEATHER  REVIEW. 

TABLE  56. — Velocities. 


472 


» _    ^l8^8    T  rj°l" 

37.20      B"k' 
523.6       T.^, 
9T300      £  ~F' 
2  _     4188.8   B9  T^  rpy 
~~    (U0356  7i    2;    A 


iv*  = 


523.6 


w  = 

w  = 

10.610 
7.503 
201.12 

1 

k 

Logs. 
[1.02578]. 

[0.87526]. 
[2.30345]. 

[2.15294]. 

VI 

'•  /"«, 

VI 

Dpw 

I 

k 

VJ 

T 

4 

.»  /  o 

'     £) 

1 

0.02589  5    T.    fc    ' 

—  o 

Units.     Ceutimeter-gram-second.     (C.  G.  S. ) 
Taking  B,  r,  and  Z>  in  centimeters,  />„,  in  grams,  the  velocities  then  become, 

-=  10.610^/^^4 


(36)     Velocity  in  meters  per  second. 

(37) 

(38) 

(39) 


w=    7.503 


to  =  20.112  J"° 


r^J-20.112 


=  14.221.  l~'~ 


Application  of  formula  (37);  w  in  meters  per  second. 


w  =  7.503  /  j 

RainPu,  =  l. 

Hail 
p.,  =  0.917. 

1  Friction  factor. 

Height 
in  meters. 

B 

T 

D 

JD 

D 

/Ti  — 

k 

*? 

273 

283 

293 

qnq 
OUO 

313 

*f  °fw 

0.          

CHI. 

76.00 
67.51 

60.25 

53.28 
47.34 

42.16 

37.37 
33.20 
29.59 

in.  p.  s. 
14.22 

15.09 
16.01 

16.99 
18.02 

19.12 

20.28 
21.52 
22.83 

m.p.s. 
14.48 

15.36 
16.30 

17.29 
18.35 

19.47 

20.65 
21.91 
23.24 

m.p.s. 
14.73 

15.63 

16.58 

17.60 
18.67 

19.81 

21.01 
22.29 
23.65 

m.p.  s. 
14.98 

15.90 
16.87 

17.89 
18.98 

20.14 

21.37 
22.67 
24.06 

m.p.  s. 
15.23 

16.16 

17.14 

18.  19* 
19.  29) 

20.47 

21.72 
23.06 
23.44 

cm. 
1.00 
0.90 

1.00 

0.95 
0.89 
0.84 
0.78 
0.71 
0.63 
0.55 
0.45 
0.32 
0.22 
0.10 
0.03 

cm. 
10 
9 
8 
7 
6 
5 
4 
3 
2 
1 

3.03 
2.87 
2.71 
2.53 
2.35 
2.14 
1.90 
1.66 
1.35 
0.96 

1.0 
1.1 
1.2 
1.3 
1.4 
1.5 
1.6 
1.7 
1.8 
1.9 

1.00 
0.95 
0.91 
0.88 
0.8S 
0.82 
0.78 
0.77 
0.75 
0.73 

1000 

2000              

0.  80 
0.70 
Large  drops  0.  60 
0.50 
0  40 
Common  drops.  0.30 
0.20 
0.10 

Fine  drops....  »'  <* 
1.0.001 

3000 

4000    

5000  

6000              

7000            

8000  

TABLE  57. — Conversion  factors  for  units  of  length,  mass,  and  pressure. 


Meter-kilogram-seconds. 

Decimeter-gram-seconds. 

C'entimeter-gram-seconds. 

Foot-pound-seconds. 

Inch-grain-seconds. 

Number. 

Logarithm. 

Number. 

Logarithm. 

Number. 

Logarithm. 

Number. 

Logarithm. 

Number. 

Logarithm. 

Length, 

1  meter. 

0.00000 

10 

1.00000 

100 

2.00000 

3.2808 

0.51599 

39.37 

1.59517 

/;. 

0.1 

9.00000 

1  decimeter. 

0.00000 

10 

1.00000 

0.32808 

9.51599 

3.937 

0.59517 

0.01 

8.00000 

0.1 

9.00000 

1  cm. 

0.00000 

0.  032808 

8.51599               0.3937 

9.  59517 

0.  3048 

9.  48402 

3.048 

0.  48402 

30.48 

1.  48402 

1  foot. 

0.00000             12.0 

1.07918 

0.  0254 

8.  40484 

0.254 

9.  40484 

2.54 

0.  40484 

0.  08333 

8.92082 

1  inch. 

0.00000 

Mass, 

1  kilogram. 

0.00000 

1000 

3.00000 

1000 

3.00000 

2.  2046 

0.  34333 

15432.  4 

4.  18843 

If. 

0.001 

7.00000 

1  gram. 

0.00000 

1 

0.00000 

0.  0022046 

7.34333             15.4324 

1.  18843 

0.001 

7.  00000 

1 

0.00000 

1  gram. 

0.00000 

0.0022046 

7.34333             15.4324 

1.18843 

0.  453593 

9.  65667 

453.  593 

2.  65667 

453.  593 

2.65667 

1  pound. 

0.  OO(KX) 

70(10 

3.  84510 

0.  000064799 

5.81157 

0.  064799 

8.81157 

0.064799 

8.81157 

0.  00014286 

6.  15490 

1  grain. 

0.00000 

Pressure, 

1  kilo.  /m.< 

0.00000 

in 

1.00000 

0.1 

9.00000 

0.  20481 

9.31135 

9.  9562 

0.99809 

,  _.v 

0.1 

9.00000 

1  gram/dm.  - 

o.oooon 

0.01 

8.00000 

0.  020481 

8.31135 

0.  99562 

9.  99809 

'    /,«• 

10 

1.  00000 

100 

2.  0001  III 

1  gram/cm.2 

0.00000 

2.0481 

0.31185             99.5620 

1.  99809 

4.3323                  0.63363 

43.  823 

1.  63363 

0.  18323 

9.  68363 

llb./ft" 

0.00000           13.6110 

1.  63671 

0.10044 

9.00189 

1.0044 

0.00189 

0.010044 

8.00189 

0.020571 

8.00000         1  gr.  /in.  - 

0.00000 

473 


MONTHLY  WEATHER  REVIEW. 

TABLE  58. — Conversion  factors  for  units  of  dMtmcr,,  time,  and  velocity. 


OCTOBER,  1906 


1  llil^. 

Mi  t<Ts  per  second. 

Kilometers  per  hour. 

Miles  per  hour. 

Feet  i>'  r  srroml. 

Number. 

Logarithm. 

Number. 

Logarithm. 

Number. 

Logarithm. 

Number. 

Logarithm. 

DistatK-e, 
& 

1  meter 
1000. 
1609.  :i!5 
0.  304794 

0.00000 
3.00000 
a  20664 
9.48400 

0.001 
1  kilometer. 

i  ww.-n.-. 
0.  00030479 

7.00000 
0.00000 
0.20664 
(1.  48400 

0.00062188 

0.  62138 
1  mile. 
0.0001894 

i;.  7'.c:iti 
:i.  7!i:i:;n 
0.  OOIKK) 
0.27737 

8.  MM 
8280.9 

5280. 

i  r.H.t. 

0.51000 
1.51600 

3.  72263 
0.00000 

Time. 
T. 

1  second 
3600 
3600 

1 

0.00000 
3.55630 
3.55630 
0.00000 

0.  0002778 
1  hour. 
1 
0.  0002778 

6.44370 
0.00000 
0.00000 
6.  44370 

0.  0002778 
1 
1  hour. 
0.  0002778 

i;.  41:170 
0.00000 
0.00000 
6.  44:(70 

i 
MM 

3600 
1  second. 

0.00000 
3.55630 
8.H6SO 

0.00000 

Velocity, 
'-£ 

1  m.  /sec. 
0.  2778 
0.  4470 
0.3048 

0.00000 
9.44:i7" 
9.  65034 
9.48400 

3.600 
1  kilo.  /hour. 
1.6093 
1.0973 

0.55630 
0.00000 

0.2(16111 
0.04030 

2.2369 
0.  6215 
1  mile/hour. 
0.6818 

0.  34966 
9.  79335 
0.  00000 
9.  83367 

3.2809 
0.9113 
1.4666 
1  ft.  /sec. 

0.  51600 

t.Msm 

0,  16633 
0.00000 

TABLE  59. — Conversion  factors  for  pressures  and  velocities. 


Pounds  /  foot2.         Miles  /  hour. 
Ap  =    1  cv* 


Kilogr.  /  met.2. 

Ap   =    4.8823  cr* 


Feet  /  second. 
=    (0.6818)"  ei',1 
0.4649 
[9.66734]  log 


Meters  /  second. 
(2.2369)' cr/ 
5.004 
[0.69932]  log 


=     4.882  x  (0.6818)'  cvs*  =     4.882  (2.2369)'  crs2 
2.270  24.43 

[0.35597]  log  [1.38795]  log 

Grams  /  cm.*. 

Ap  =    4.8823 X  0.1  cr,2 

0.2270 

[9.35597]  log 
Grains  /  inch2. 

Jp   =    4.8823 x  9.9562  cv*  =  48.61  (0.6818)'  cv* 
48.61  22.CO 

[1.68674]  log          [1.35408]  log 
Grams  /  dm.*. 

Ap  =    4.8823  x  10  cr,,2         =  48.823  (0.6818)'  cv*     =  48.823  (2.2369)' cr3' 
48.823  22.697 

[1.68863]  log         [1.35597]  log 


0.4882  (0.6818)2 cv*  =     0.4882  (2.2369)2  crs2 

2.443 

[0.38795]  log 

=  48.61  (2.2369)'  cv* 
243.3 

[2.38606]  log 

48.82? 
244.32 

[2.38795]  log 


Kilometers/  hour. 
(0.6215)acu4* 
0.3861 

[9.58672]  log 

4.882  (0.6215)' cr' 
1.885 
[0.27535]  log 

0.4882  (0.6215)' cr,' 
0.1885 
[9.27535]  log 

48.61  (0.6215)'  cr,1 
1.877 
[0.27346]  log 

48.823  (0.615)" m* 
18.852 

[1.27535]  log 


c  represents  the  other  terms  in  the  general  formula  for  J  p. 
The  numbers  inclosed  in  brackets  are  logarithms  of  the  factors  accurately  computed. 


TABLE  60. — Resistance  to  a  solid  moving  in  a  jluid. 
Newton's  theorem  and  the  coefficient  k. 

p  =  density,  h  =  height,  w  =  vertical  velocity,  A  =  Area. 
The  resistance  between  the  solid  and  fluid  is  equal  to  the  pres- 
sure due  to  the  weight  of  a  column  of  the  fluid  p  h  A  =  pN , 

10*                              10* 
where  w1  =  Zgh,tindh=  ~— ,  so  that  px=  p-^-.  A (21). 

By  observations  this  requires  a  coefficient  k=  -*• . 

PN 


On  account  of  viscosity  and  other  forces  the  more  complete 
formula  is  p  =  aw  +  bio*  +  cw*  +  .  .  . . 

For  air  blowing  against  a  plate  normally  there  is  an  excess 
of  pressure  -f  Jp,  on  the  front  side,  and  a  defect  of  pressure 
—  Jp2  on  the  back  side  of  the  plate. 

Take  the  static  pressure  of  the  air  on  the  body  =  p. 


(42)     Wind  pressure  =  pt  —  p2  =  Jj>=  +  J/^ 


TABLE  61.  —  Differential  coefficients. 

n 

From  (24)  J/>  =  c.  k  fpiir  .     c=  constant. 


(43) 


(40)     Front  side  pressure  =  p^  =  p  +  Jpl=p  -\-  kl  f>  „    A 


w 
>  „ 


(41)     Back  side  pressure  =  />2  =  p  —  ^P,=P  —  &,  p  «-  A 


(45) 


(46). 


fc=  coefficient  of  resistance  =  1.30. 

=  77  die.     Increase  J  k  =  +  0.1  ; 
increase  J/>=  1.1%. 

=  0.13  dlimm.'  Inc.  JB  =  +  1 """ ; 
increase  J/-=  0.13%". 

•--™°3dT=-0.37dT.  Decrease  J  7'= -1°; 


100  di, 
1.3 

100  . 


.  100 


ncrease  J]>  = 


100  dlr 


OCTOBER,  1906. 


MONTHLY  WEATHER  REVIEW. 


474 


ck 


100  d  B 


(47) 


(48) 


ck    T  tt>2 
,  B 


760 


1  OIK/7' 
27:: 


(49)     From  (24)  w2  = 


100  x  2 10  d  w  _ 


• 

J  >    C  .  A" 


T    1 
Ji  e.k 


WQdw  =  a^p 

w        2  J  p 


(60) 
(51) 

(52) 
(63) 

(54) 

(55)  Maxwell.     //= 0.000  000  0256(461' 


1  %  error  in  J  ;)  =  i  %  error  in  w. 

1  rfT  100  =  0.18  dl7. 

2  273 

1°  error  in  T  =  0.18  %  error  in  w. 


1  f//y  100  =  —0.07  dB. 

2  760 

!»"»  error  in  B  =  —  0-07  %  error  in  w. 

1   rf£ 
~2   L3 

0.1  error  in  k  =  —  3.8  %  error  in««. 

TABLE  f  2.—  Coefficient  of  viscosity  for  air,  /t. 

, pound      1 

foot*   '  foot 

The  pressure  in  pounds  required  to  slide  1  square  foot  of 
air  at  the  rate  of  1  foot  per  second  parallel  to  a  layer  1  foot 
distant,  when  the  temperature  in  Fahrenheit  degrees  is  t. 
Maxwell.         //=0.000  1878  (1  +  .00275 1),  G.  G.  S.  units. 
O.  E.  Meyer.         0.000  1727. 

Compare  Basset's  Hydrodynamics,  Vol.  II,  p.  251. 
Coefficient  of  resistance  for  air,  k. 


56)  Poncelet 

and 
Unwin. 


Coefficient  k 

1.85 


A      section  of  the  current 
~~  a         section  of  the  body 
_  a,      section  of  contracted  current 

a  ~  section  of  the  body 

For  circular  plates. 
Morin.  For  plates  1  foot  square. 

Thibault.      For  plates  0.3  to  0.5  meter  square, 

velocity  2  to  8  meters  per  second. 

Dvichemin.    Reduction  of  rectilinear  motion  to  circular  motion. 
p  =  pressure  for  rectilinear  motion  with  velocity  i'. 
pc  =  pressure  for  circular  motion  with  velocity  u. 
A  =  area  of  greatest  section  of  the  body. 
I*  =  density  of  the  fluid. 
B  =  arm  of  rotation  at  the  center  of  A. 
x  =  distance  of  center  of  figure  of  A  from  the  center 
of  gravity  of  the  half  section  of  A  on  side  of  axis. 
i  =  angle  of  incidence  of  air  striking  the  front  of  A. 
ft  =  i  */  A  •  si11  *  =  thickness  of  the  flowing  stream  on  A. 


(57) 


1.30 
1.36 

1.83 


For  plane  surfaces        

(  1.25 

(  1.30 

Mariotte. 

Plates  with  low  velocities. 

1.74 

Weissbach. 

Fixed  plates  in  a  moving  current  of  air. 

1.25 

( 

1.19 

Woltinann. 

Experiments  at  Hamburg,  1785-1790  •( 

1.49 

( 

1.34 

Munche. 

From  experiments  of  Woltmann,  de  Borda, 

Hutton. 

1.30 

Dubuat. 

Grashof's  discussion. 

1.43 

0  565 

Didion. 

k=  1.318+  r^-  . 

1.32 

w~ 

Hutton. 

Sphere  for  velocities  under  90  meters  per 

second,  using  a  ballistic  pendulum. 
Nordmark.    Double  conical  bodies. 
Cylindrical  bodies. 
Spherical  bodies. 

Piobert.  ]      In  joint  experiments  with  plates  0.5  to  1.0 
Morin.  meter  square,  velocities  0  to  9  meters 

Didion.    )          per  second. 

Poncelet.       Recommends  as  the  result  of  discussing  all 
data  available  to  him. 


1.40 

0.67 
0.91 
0.83 


1.357 

1.30 
1.39 
1.49 
1.64 

1.24 
1.43 


1.85 

1.15 
1.23 

1.90 

1.84 


De  Borda.  Whirling  machine,  plates  0.10  to  0.03  square 
meter,  velocity  3  to  4  meters  per  second. 

Hutton.  Using  Robbin's  whirling  machine,  plate 
0.01  to  0.02  square  meter,  and  velocities 
up  to  6  meters  per  second. 

Rouse.  Whirling  machine.    Pressure  in  pounds  per 

foot2,/>  =  0.00492  if.  Velocity  in  miles  per 
hour. 

Beaufoy.  Whirling  machine,  plate  1  foot  square,  ve- 
locity 2  meters  per  second,  and  for  a 
larger  plate. 

Prechtel.       Square  plate rotatiugaroundoneedgeasaxis 

Rouse.  And  the  Royal  Meteorological  Society. 

Hagen.  Whirling  machine  with  disks  which  were 

square,  circular,  and  triangular,  the  av- 
erage circumference  being  0.50  meter, 
and  velocities  between  1.5  and  5.5  feet 
per  second. 

For  C=  circumference  of  the  area  A  =  0.50 
meter. 

(58)  Jp=  (0.00707  +  0.0001125  C)A  v*  (gram- 

decimeter  second). 

Ap=  (0.0707  +  0.01125  C)  A  t;2  (kilogram- 
meter  second). 

Jp  =  (0.0028934+ 0.0001403  G)  A  u2  (uin 
miles  per  hour,  p  in  pounds,  C  in 
feet,  and  A  in  square  feet). 
From  these  results, 

k  =  1.135+0.1805  C  =  1.135  +  0.090.      1.225 

Thiessen       Whirling  apparatus  with  cylindrical  bars, 
and  D  =  diameter  2  to  3  millimeters,  L  = 

Schellbach.  length  0.3  to  1.0  meter'. 

(59)  Ap  =  (7.25  u  +  0.486  D  v* 

+  0.0000698  Z>2  us)  10    L,  (C.  G.  S). 
J  p  =  (0.0000725  i'  +  0.0486  D  u2 
+  0.0698  D2  us)  L,  (M.  K.  S). 
For  B  —  760  millimeters,  and  t  =  20  °C, 

k  =  0.00118  JL  +  0.7914  +  1.1366  Dv 
Dv 

(for  cylinders). 

k=  0.00154 A  +  1.008  +  1.448    Dv, 
Dv 

(for  squares). 


475 


MONTHLY  WEATHER  REVIEW. 


OCTOBER,  1906 


Thiebault. 


Langley. 

Nipher. 
Dines. 


k  =  0.546  1  +  1.008  +  0.0040  v 
v 

(for  D  =  0.00275  m). 
k  for  average  velocities.  1.300 

Thin  plates  on  a  whirling  machine. 

Square  plate,  4=0.026  square  meter.  1.525 

Square  plate,  4=0.10304  square  meter.  1.784 

Rectangular  plate,  4=0.10304,  long  side  1.900 

radial. 

Rectangular  plate,  4=0.10304,  short  side  1.677 

radial. 

Square  plate,  4  =  (0.323)2,  radius=  1.370.  1.784 

Square  plate,  4=(0.227)2,  radius=0.966.  1.784 

Square  plate,  4  =  (0.161)2,  radius=0.685.  1.784 

Whirling  machine,  square  plate  with  veloci- 
ties 4  to  11  meters  per  second.  1.31 
Railroad  car  direct  wind  pressures.                  1.37 


Stokes. 


route 


FIG.  38. — Special  form  of  whirling  apparatus  used  by  Dines. 

W=  weight  of  adjustable  piece. 
a>0  =  angular  velocity  of  rotation  of  W  about  C. 
The  piece  P  B  W  is  rigid  and  by  its  rotation  about  B 
assumes  a  position  of  equilibrium. 

For  equilibrium. 


(60) 


(61) 


Px=k  23.68  ™  (r+a;)'<«0J4.;r=7r  cos  <?.y. 


cos  <f  .  y  =  — 
9 


k  = 


W 


W       ry 


23.685  '    g  (r+x)*x     A 
Ap  kil.  /  met,'=  A  v3  =  H  (20.86)'  mile  /  hour  =  A  (9.3)s  meter  /  sec. 


_ 
0.06o93  ir 


Squares 


Rectangles 


4x    4  inches 

8x  8 
12x12 
16X16 

1*6  x  1  inches 
16x  4 
24x  6 


0.  00347 
340 
361 
350 

0.  00391 
363 
366 


Circular  plates  4.  51  inches  in  diameter  0.  00347 

6.  00  338 

9.  03  345 

13.  54  357 


k 

1.  29 
1.27 
1.34 
1.30 

1.45 
1.35 
1.36 

1.29 
1.  25 
1.  28 
1.  32 


Mean  0.  00355  Mean   1.  32 

(62)       A  p  =  0. 00355  u2  (pound  /  foot2,  and  mile  /  hour). 
^=281.7  Jp__ 
v  =  16.78         ~ 


The  resistance  to  any  moving  body  immersed 
in  a  fluid  is  composed  of  two  parts. 

1.  That  due  to  viscosity  and   proportional 
to  v  is  av. 

2.  That  due  to    gyratory  motions  varying 
with   the  v-  and   the  boundaries  of  the 
fluid  is  6tA 

The  second  may  disappear  in  slow  motion 
but  the  first  remains  appreciable. 

=  coefficient  of  viscosity  div.  by  density. 
r    =  radius  of  sphere. 


(63) 


Jp=  6  TT 


v  inch/second. 


Stokes  finds  //  =  />  (0.116)2  for  air. 
The  maximum  velocity  of  a  falling  body  be- 
comes permanent  when, 


pw  =  density  of  the  sphere. 

/i     =  density  of  the  fluid  thru  which  it  falls. 

g     =  acceleration  of    gravity    in   inches, 

386  inches. 
iu    =  velocity  inch/second: 

1  inch/second  =0.0254  meter/second. 
For  small  drops  of  water  at  small  velocities 
the  viscous  resistance  of  the  air   is  far 
larger  than  the  impact  resistance,  as  com- 
puted by  the  Newtonian  theorem. 
For  r  =  0.0005  inch,  water  />u,  =  1,  air  in  the 
lower  clouds,  p  =0.001,  we  find  wm=  1.593 
inch/second  =  0.133  foot/second. 

Recknagel.  Pressure  at  the  center  of  the  front  of  a  plane 
plate  and  at  the  apex  of  a  solid  of  revolu- 
tion. 

=  pressure  in  still  air  surrounding  plate, 
kilogram/meter2. 

—     -=  mass  of  1  cubic  meter  of  air. 
9          9 


p 


m  =    °= 


va   =  velocity  of  the  air  relative  to  center 
of  plate,  meter/second. 

Q 

-^  =  Tc  =  1.41  =  ratio  of  specific  heats. 
" 


k— 1 


=  0.2908. 


=0.1754  Jp^|=  0.8564  Jp  pound/foot2.     (65) 


Pi  =  P  (1  + 


J, 1      ,.2 

IS.   IS] 

*  *Vp, 

7?i  v  2  for  low  velocities. 


2  for  any  velocities. 


p,  =  p  +  0 

The  pressure  diminishes  from  the  center  to 
the  edge  of  the  plate. 

Schreiber.  A  discussion  of  the  distribution  of  the  pres- 
sure over  a  flat  plate  is  given  on  pages  36- 
38,  of  Studien.iiber  Luf tbewegungen,  von 
Paul  Schreiber,  Abh.  d.  Kon.  Sachs,  me- 
teorol.  Inst.  Heft  3,  1898. 

Nipher.  A  complete  experiment  of  the  distribution 
of  pressure  over  a  plate  is  given  in  his 
paper,  "A  method  of  measuring  the  pres- 
sure at  any  point  on  a  structure,  due  to 
wind  blowing  against  that  structure,"  by 
Francis  E.  Nipher,  Transactions  of  the 
Academy  of  Science,  St.  Louis,  Mo.,  Vol. 
Ill,  No.  L 
This  agrees  with  the  formula,  given  by  Hann  on  page  11,  tlber 

die  tiigliche  Drehung  der  mittleren  Windrichtung,  etc.    Wien, 

1902. 


OCTOBER,  1906. 


MONTHLY  WEATHER  REVIEW. 


476 


Table  53,  formulas  14,  15,  deduces  the  barometric  gradient 
which,  acting  along  the  meridian  from  south  to  north,  will 
jUst  sustain  the  wind  velocity  v  directed  due  eastward.  This 
is  the  formula  for  determining  the  relation  between  the  east- 
ward drift  of  the  atmosphere  in  the  upper  strata  and  the  nor- 
mal gradient  which  is  required  to  sustain  it.  This  is  also 
found  on  page  11  of  Hann's  paper  and  on  page  472  of  his 
Lehrbuch  der  Meteorologie. 

Table  54,  formulas  16-21,  contains  the  deduction  of  the 
Newtonian  theorem  for  the  pressure  exerted  by  wind  velocity 
on  a  body.  The  general  equation  becomes 

(19)  —p  =  f>W  +  !>h. 

In  case  there  is  equilibrium  between  the  weight  represented 
by  p  h  and  the  pressure  exerted  by  a  vertical  velocity  u2,  so 
that  p  =  0,  we  have 

(20)  ^=A. 

which  is  the  law  of  the  velocity  for  a  freely  falling  body. 
Hence,  the  pressure  exerted  by  the  first  term,  p  ~=py,  is  the 

Newtonian  pressure. 

From  observations  it  is  found  that  this  pressure  must  be 
multiplied  by  some  factor  k,  to  reduce  it  to  the  actual  pressure 
which  is  exerted  upon  a  rigid  body  of  sensible  dimensions. 
When  such  a  body  moves  thru  a  still  fluid,  or  when  a  moving 
fluid  passes  a  fixt  body,  the  stream  lines  of  the  fluid  are  de- 
flected in  passing  the  body,  making  an  excess  of  pressure  on 
the  front  side,  +  dpv  and  a  defect  of  pressure  on  the  back 
side,  —  Jp.2,  so  that  the  total  resultant  pressure  is 

This  is  not  equal  to  the  Newtonian  pressure,  but  differs  from 

it  by  some  factor,  k  =  Preservation)  =  P. .       The   deflection 
p  (rsewton)  p^ 

of  the  stream  lines  causes  vortices  and  hydrodynamic  pres- 
sures of  a  complicated  kind,  which  are  integrated  in  the  total 
excess  of  pressure  of  the  positive  and  the  negative  types.  Many 
experiments  have  been  made  to  determine  the  relations  be- 
tween the  front  and  the  back  pressure,  but  they  depend  largely 
upon  the  shape  and  size  of  the  body  and  the  density  of  the 
fhiid.  The  existence  of  a  diminished  pressure  and  consequent 
inflow,  or  so-called  "  suction  ",  on  the  leeward  side  of  bodies 
exposed  to  the  wind  has  been  generally  recognized,1  but  the 
experiments  of  Mr.  Irminger,  a  Danish  engineer,  made  to  de- 
termine the  amount  of  such  suctions,  shows  it  to  be  present 
to  an  unexpected  extent.  His  measurements  were  made  by 
the  use  of  hollow  plates  and  models  of  thin  sheet  iron  exposed 
in  an  air  duct  4|  by  9  inches  cross  section,  at  various  angles 
and  positions,  to  velocities  ranging  from  16  to  32  miles  per 
hour.  We  quote  the  data  from  Julius  Baier's  paper  on  wind 
pressures  in  the  St.  Louis  tornado,  American  Society  of  Civil 
Engineers,  Vol.  XXXVII,  1897,  No.  805.  (See  Table  63.) 

This  shows  that  the  percentages  vary  widely  with  the  shape 
of  the  body,  and  its  exposure  to  the  direction  of  the  wind, 
and  that  the  lee  suction  is  often  much  in  excess  of  the  front 
pressure.  For  spheres  the  front  pressure  is  28  per  cent  and 
the  back  suction  72  per  cent  of  the  total  pressure  p.  The 
total  pressure  on  a  sphere  is  only  57  per  cent  of  that  on  a  thin 
plane  having  each  side  equal  to  the  diameter  of  the  sphere. 
The  subject  is  very  complex  in  application  to  special  cases. 

'See  Abbe  in  the  Monthly  Weather  Review,  November,  1886,  Vol. 
XIV,  p.  332,  and  his  publication  of  observations  on  the  pressure  and 
suction  around  the  Weather  Bureau  station  at  Mount  Washington, 
N.  H.,  in  his  Meteorological  Apparatus  and  Methods,  pp.  142-144.  See 
also  the  results  of  experiments  on  chimneys  and  cowls,  Proc.  Am.  Acad. 
Arts  and  Sciences,  Boston,  1848 ;  Journal  Franklin  Institute,  Philadel- 
phia, 1842. 


TABLE  63. — Percentage  of  front  and  backpressures  (Irminger's  results). 


PRESSURE  IN  A 
HORIZONTAL 
DIRECTION 

PRESSURE  ON  THE 
WINDWARD  SIDE 
$TOTAL  PRESSURE 

SUCTION  ON  THE 
LEEWARD  SIDE 
<?TOTAL  PRESSURE 

["H 
,-  * 

45 

65 

n  i      <>.95p 

67 

43 

V%»J-                   0.79p 

24 

76 

O                    0-57P 

28 

72 

</<£>                   0.25p 

18 

82 

jAf                    0.59p 

68 

42 

<£]•                  0.42p 

14 

86 

«£>                    0.71p 

63 

37 

The  wind  velocities  are  usually  taken  in  the  United  States 
by  the  Robinson  anemometer,  but  the  indicated  velocities  must 
be  reduced  about  20  per  cent,  in  order  to  obtain  true  values 
of  the  velocity  to  enter  into  the  formula. 

The  reduction  factor  from  miles  per  hour  to  meters  per 
second  is  as  follows: 

1  mile  per  hour  =  0.4470  meter  per  second. 

MARVIN'S  CORRECTION  TO  OBSERVED  WIND  VELOCITIES. 

The  velocity  of  the  wind  is  very  generally  measured  by  some  form  of 
the  Eobinson  cup  anemometer.  From  early  experiments  it  was  found 
that  the  distance  passed  over  by  the  center  of  one  of  the  revolving  cups 
would,  if  multiplied  by  three,  give  the  velocity  of  the  wind,  and  the 
wheels  and  recording  dials  of  the  instrument  were  geared  to  read  wind 
velocities  directly  by  taking  into  account  this  factor  of  reduction.  Later 
experiments  have  shown  that  with  anemometers  of  the  size  commonly 
used  this  ratio  is  erroneous,  and  the  indicated  velocities  are  about  20  per 
cent  too  great,  but  no  change  has  been  made  in  the  recording  device  and 
the  "  wind  observations  published  by  the  various  meteorological  institu- 
tions at  the  present  time  have  only  a  relative,  but  not  absolute,  value. 
It  is  very  probable  that  many  experiments  on  the  relations  of  wind 
velocities  to  wind  pressures  have  been  made  in  which  this  anemometer 
correction  has  not  been  properly  applied  ". 

Professor  Marvin  has  determined  the  correction  to  be  applied  to  the 
readings  of  the  standard  form  of  anemometer  used  by  the  Weather 
Bureau.  It  is  expressed  by  a  logarithmic  formula  from  which  the  follow- 
ing table  taken  from  his  report  on  wind  pressures  is  computed: 

TABLE  64.— Corrected  wind  velocities  as  indicated  by  a  Robinson  anemometer, 
in  miles  per  hour. 


Indicated  velocity. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0                          

6.1 

6.0 

6.9 

7.8 

8.7 

10          

9.6 

10.4 

11.3 

12.1 

12.9 

13.8 

14.6 

15.4 

16.2 

17.0 

20                            

17.8 

18.6 

19.4 

20.2 

21.0 

21.8 

22.6 

23.4 

24.2 

24.9 

30           

25.7 

26.5 

27.3 

28.0 

28.8 

29.6 

30.3 

31.1 

31.8 

32.6 

40 

33.3 

34.1 

34.8 

35.6 

36.3 

37.1 

37.8 

38.5 

39.3 

40.0 

50                                       .    ..  . 

40.8 

41.5 

42.2 

43.0 

43.7 

44.4 

45.1 

45.9 

46.6 

47.8 

60            

48.0 

48  7 

49.4 

50.2 

50.9 

51.6 

52.3 

53.0 

53.8 

54.5 

70 

55.2 

55  9 

56.6 

57.3 

58.0 

68.7 

59.4 

60.1 

60.8 

61.5 

80                     

62.2 

62.9 

63.6 

64.3 

65.0 

65.8 

66.  1 

67.1 

67.8 

68.5 

69  2 

Total  velocity  =  number  on  side  and  number  on  top  of  same  column.     Thus,  for  41  the 
corrected  velocity  is  34.1;  for  57  the  corrected  velocity  is  45.9. 

Table  55,  formulas  22-31,  contains  the  formulas  for  the 
vertical  velocity  that  just  sustains  a  freely  falling  body.  The 
successive  steps  are  clearly  indicated.  In  formula  24  the  co- 
efficients are  computed  for  the  value  of  k  =  1.3  employed 
by  Professor  Schreiber.  Since  the  weight  of  a  body, 
Wg=.  ^xr'p  x  1000  kilograms,  must  be  put  equal  to  JpA  = 
4  B  <rm  \  ff  r2  for  equilibrium  under  the  specified  conditions, 
further  formula  can  be  developed.  The  area  A  in  (23)  is 


477 


MONTHLY  WEATHER  REVIEW. 


OCTOBER,  1906 


taken  as  equivalent  to  half  the  greatest  cross  section,  so  that 
A  =  |  T:  r-  =  \  -  !>'-.  According  to  Irininger's  tests  the  coeffi- 
cient of  -r°  should  be  0.57  instead  of  0.50.  The  specific 

weight  of  the  body  =/<„  =  ''">  where  the   specific  weight  of 

Pi 
water  is  the  unit.     The  density  of  the  air  at  any  point  is 

li   T 
found  by  the  usual  formula  p  =  pa  -&  „," .      Formulas   28-31 

•**•  •* 

contain  the  several  relations  found  by  putting  (24)  in  combi- 
nation with  (25). 

Velocities. 

Formulas  32-35  of  Table  56  contain  the  resulting  velocities 
in  the  kilogram-meter-second  system  (M.  K.  S.).  In  the  cen- 
timeter-gram-second  (C.  G.  S.)  system  for  the  barometric  pres- 
sure B,  the  radius  r,  and  the  diameter  D  in  centimeters,  for 
the  density  f>  in  grams,  and  the  velocity  in  meters  per  second, 
we  have  the  values  of  the  velocity  w,  as  given  in  formulas 
36-39.  Formula  36  gives  the  velocity  in  meters  per  second 
in  terms  of  the  absolute  temperature  T,  the  barometric  pres- 
sure B  in  centimeters,  the  radius  of  sphere  in  centimeters,  the 
specific  weight  of  the  body  in  grams.  The  coefficient  k  must 
be  assigned  from  experimental  data.  Formula  37  employs  the 
same  data  as  36  except  that  the  diameter  is  used  instead  of  the 
radius.  Hence,  10.61  =  7.503  x  v/2  and  20.112  =  14.221  x  v/2. 


T*         /TT 

In  38  and  39  the  substitution     ° 

D 


-?  is  made,  in  case  one 
o      P 

prefers  to  use  the  densities  rather  than  the  pressures  and 
temperatures.  We  have  taken  formula  37  for  development 
and  application  to  the  formation  of  hail. 

IT        i' 

Formula  37, 10  =  7.503A/     Dp,-     The  first  section  of  the 
\B       w  k 

table  contains  w  =  7.503    /_£  for  the  arguments  T  and  B.     T 

begins  at  273°,  since  in  hail  formation  the  temperature  does 
not  fall  below  0°  C.,  and  it  extends  to  T=  313°,  which  is 
the  extreme  of  summer  heat  at  the  surface.  Approximate 
values  of  B  are  taken  at  the  heights  H  as  indicated,  so  that 
H  or  B  may  be  used  in  practical  applications.  If  D  =  1  cen- 
timeter, pw  =  1  for  water,  and  k  =  1,  the  velocity  in  meters  per 
second  is  found  in  the  body  of  the  table.  In  application  to 
water  drops  of  various  sizes,  large  drops  0.70  to  0.50  cm., 
common  drops  0.40  to  0.20  cm.,  fine  drops  0.100  to  0.001  cm., 
the  subjoined  multiplying  factor  x/J9  must  be  used.  In  the 
case  of  hail,  for  pw  =  0.917,  the  tabular  factor  ranges  from 
D  =  10  cm.  to  D  =  1  cm.  giving  the  several  values  of 


It  is  shown  in  the  following  tables  that  the  coefficient  k  is 
equal  to  about  1.30  for  bodies  of  considerable  dimensions, 
such  as  engineers  naturally  employ,  plates,  disks,  spheres, 
cubes,  and  parallelepipeds  placed  on  whirling  machines  for 
tests.  These  can  hardly  be  true  for  water  drops  which  are 
not  rigid,  but  very  flexible  in  their  form  while  falling,  since 
they  undergo  periodic  changes  in  shape  when  in  motion,  like 
oil  drops  rising  in  water.  It  is  difficult  to  assign  values  to  k 
for  fluids,  and  on  that  account  the  factor  has  been  kept 
separate  from  the  first  section  of  the  table.  My  opinion  is 
that  k  =  1.1  nearly  for  water,  but  that  on  the  solidification 
into  hail,  the  value  of  k  approaches  k  =  1.30,  in  consequence 
of  its  rigid  shape  in  the  solid  state,  which  is  of  dimensions 
comparable  with  those  used  in  the  physical  experiments. 
These  tables  can  be  readily  used  in  numerous  combinations, 
by  selecting  the  suitable  sets  of  factors  to  be  multiplied  to- 
gether. The  effect  of  k  is  to  diminish  the  required  velocity 
w  in  meters  per  second,  since  the  form  of  the  body  generates 
a  term  which  is  itself  equivalent  to  an  addition  to  the  actual 


wind  velocity.  The  required  velocity  increases  with  the  di- 
mensions of  the  body,  and  with  the  increase  of  density  of 
bodies  of  the  same  dimensions. 

Convention  fartorx. 

Tables  57,  58,  and  59  contain  the  conversion  factors  between 
several  systems  of  vinits  which  are  found  in  the  papers  relating 
to  the  velocities  and  pressures.  Table  57  gives  the  units  of 

length  L,  the  units  of  mass  M,  the  pressure  p  =  — , .    Table  58 

gives  the  distance  S  traversed  in  the  unit  of  time,  the  unit  of 

t< 

time  T,  the  velocity  V=  l  .  Table  59  gives  various  combina- 
tions between  the  pressure  and  the  velocities  for  several  sys- 
tems of  units.  For  example,  the  pressure  in  pounds  per  square 
foot  with  the  velocity  in  miles  per  hour,  becomes  the  pressure 
in  grams  per  square  centimeter  with  the  velocity  in  meters 
per  second,  by  multiplying  with  the  factor  2.443  (logarithm  = 
0.38795).  The  inverse  reduction  is  performed  by  multiplying 

with  ~-  =  0.4093  (logarithm  =  9.61205). 

Resistance  to  a  solid  moving  in  a  fluid.    ' 

The  problems  in  hydrodynamics  relating  to  solids  moving 
in  a  fluid,  or  to  a  fixt  solid  in  a  moving  fluid,  are  very  numer- 
ous and  their  discussion  can  be  found  in  several  treatises.  In 
Table  60,  formulas  40  to  42,  the  Newtonian  theorem  is  re- 
sumed in  connection  with  the  factor  k.  But  it  was  shown 
that  there  is  a  factor  kl  for  the  front  side  of  a  plate  or  solid  of 
any  form,  and  a  factor  A"a  for  the  back  side  of  this  body.  The 
wind  pressure  is  made  up  of  two  parts  Ap  =  J/>,  +  Jjos,  and 
the  factor  k  of  two  parts  k  =  fc,  +  kf  These  must  be  de- 
termined for  special  objects,  and  their  values  can  not  be 
assigned  from  general  considerations. 

Differential  coefficients. 

The  variations  of  pressure  dp  depend  upon  changes  in  the 
barometer  height  J  B,  the  temperature  J  T,  the  coefficient 
Jjfc,  and  the  velocity  J  w.  Table  61,  formulas  43  to  54,  contains 
the  differential  coefficients,  and  the  corresponding  changes  of 
the  terms  in  percentages.  Thus — 

-(-   0.1  J  fc  =  7.7  %Jp. 

+  1°"°  JB= 

-1°     JT= 

1  %  error  in  A  p  —  0.5  %  error  in  n: 

1°     error  in    T    =  0. 18%  error  in  u: 

jmm  error  jn  ft     _  0.07%  error  in  n: 

0.1    error  in    k     =3.8  %  error  in  ic. 

These  values  of  the  ratios  are  convenient  in  estimating  the 
mutual  changes  which  take  place  among  these  quantities. 

The  resistance  coefficient  k. 

It  is  evident  that  an  error  in  the  value  of  the  resistance  co- 
efficient k  is  much  more  efficient  in  producing  an  error  in  the 
wind  velocity  as  computed  than  are  similar  errors  in  the  de- 
termination of  the  barometric  pressure  and  temperature.  It 
is,  therefore,  important  to  discuss  the  coefficient  k  with  much 
care,  and  to  pass  in  review  the  results  of  the  experiments 
which  have  been  executed  for  the  purpose  of  establishing  its 
value  under  different  conditions.  These  involve  bodies  of 
different  sizes  and  shapes,  carried  thru  fluids,  such  as  air  and 
water,  with  variable  velocities.  The  experiments  extend  thru 
the  past  century,  and  many  of  them  bave  been  executed  with 
all  possible  care  as  to  details,  in  order  to  secure  scientific 
precision.  Summaries  of  these  studies  may  be  found  in  Abbe's2 

'Treatise  on  Meteorological  Apparatus  and  Methods,  by  Cleveland 
Abbe,  Appendix  46,  Annual  Report  Chief  Signal  Officer,  1887,  pages  218- 
240.  Mechanics  of  the  Earth's  Atmosphere,  C.  Abbe,  Translation  of 
Hagen's  paper,  Smith.  Misc.  Coll.,  843,  1891. 


OCTOBER,  1906. 


MONTHLY  WEATHEK  REVIEW. 


47H 


and  in  Schreiber's3  compilations  to  which  I  am  chiefly  indebted 
for  the  accompanying  data.  The  original  papers  are  enumer- 
ated therein,  and  the  bibliography  need  not  be  repeated  in 
this  place. 

Table  62,  formulas  55  to  65,  contains  the  summary  of  values 
of  k,  together  with  a  brief  statement  regarding  the  nature  of 
the  experiments  and  the  fundamental  formulas  of  the  instru- 
mental work.  Formula  55  gives  Maxwell's  value  of  the  co- 
efficient of  viscosity  in  British  units  and  in  C.  G.  S.  units,  with 
reference  to  Basset's  Hydrodynamics.  Formula  56  gives 
Poncelet  and  Unwin's  equation,  which  takes  account  of  the 
contraction  and  expansion  of  the  stream  lines  in  passing  by  a 
body.  Formula  57  gives  the  equation  for  transforming  the 
pressure  on  a  body  moving  rectilinearly  into  that  encountered 
by  it  when  carried  on  a  whirling  machine.  The  group  of  equa- 
tions under  formula  58  contains  Hagen's  restilts  in  (C.  G.  S.,) 
(K.  M.  S.),  and  (P.  F.  S. )  units,  respectively.  It  is  to  be  ob- 
served that  a  Considerable  factor  depends  upon  the  circum- 
ference of  the  plates,  and  that  the  value  of  k  =  1.104,  when 
the  circumference  is  very  small,  as  in  raindrops.  Formula  59 
contains  the  result  of  Thiessen's  and  Schellbach's  experiments 
on  long  cylindrical  rods  whirled  by  a  machine,  and  it  shows 
that  there  is  a  complex  function  depending  upon  the  first  and 
second  powers  of  the  velocity  which  is  involved  in  the  coeffi- 
cient of  resistance.  Formula  60  gives  the  equation  for  equi- 
librium in  Dines's  machine,  which  has  a  special  device  for 
determining  the  pressure  (fig.  38).  The  rectangular  arm 
I'  K  W  is  rigid  and  rocks  upon  the  axis  B;  the  arm  B  W  is 
stayed  between  two  stops,  with  electric  contact,  so  that  the 
length  of  the  working  arm  for  W  can  be  accurately  adjusted 
to  the  whirling  pressure  P  on  the  plate  A.  Formula  61  gives 
the  equation  for  k  and  the  accompanying  table  of  values  for  / 
and  I:  /  is  the  coefficient  required  to  find  the  pressure  in 
pounds  per  square  foot  from  the  velocity  in  miles  per  hour, 
and  it  averages  ).  =  0.00355,  which  appears  in  formula  62, 
Jp  =  0.00355  D2.  Professor  Marvin  has  established  the  value 
for  the  Weather  Bureau  />.  =  0.00400,  from  which  Jp  =  0.00400u2. 
Professor  Nipher  has  determined  the  value  A  =  0.00251  on  the 
windward  side  alone,  so  that  from  Irminger's  experiments  we 
are  safe  in  taking  the  total  value  as  that  given  by  Dines  or 
Marvin  for  general  conditions.  The  result  of  Stokes's  investi- 
gation on  the  resistance  of  any  moving  body  immersed  in  a 
fluid  shows  that  it  consists  of  two  parts,  the  first  due  to  vis- 
cosity proportional  to  the  velocity,  and  the  second  due  to  the 
gyratory  motions  which  are  generated  in  the  fluid  under  the 
existing  conditions,  proportional  to  the  square  of  the  velocity. 
Formula  63  gives  Stokes's  equation  and  the  value  of  <i.  for  air, 
with  a  velocity  v  in  inches  per  second.  There  are,  however, 

"Studien  tiber  Luftbewegungen,  von  Paul  Schreiber,  Adh.  d.  Kon. 
Sachs.  Met.  Inst.  Heft  3,  Chemnitz,  1898. 


other  methods  of  determining  the  viscosity  which  are  consid- 
ered better,  referred  to  in  55.  Formula  64  gives  the  maximum 
velocity  of  a  falling  body  when  it  has  become  uniform,  with  an 
example  for  a  raindrop  in  the  air.  Since  the  pressure  on  a 
large  plate  varies  between  the  center  and  the  edge  by  certain 
laws  to  be  discovered  by  experiment,  the  distribution  of  the 
pressure  has  been  discust  by  Recknagel,  Schreiber,  and 
Nipher.  Formula  65  contains  Recknagel's  equation  for  any 
velocities,  the  terms  being  specified.  For  Schreiber's  and 
Nipher's  results  reference  may  be  made  to  their  papers. 

It  will  be  seen  by  inspecting  the  catalog  of  values  for  k,  the 
coefficient  of  resistance  to  a  rigid  body  moving  in  air,  since 
the  water  experiments  have  not  been  included  in  the  list,  that 
there  is  a  great  diversity  of  data  to  be  considered  in  selecting 
a  mean  value.  This  arises  from  the  great  variety  of  condi- 
tions involved  in  the  investigations,  and  also  from  the  great 
length  of  time  covered  in  the  researches,  about  100  years.  At 
the  same  time  it  is  evident  that  they  average  closely  to  the 
value  assigned  by  Schreiber,  k  =  1.30.  This  value  applies 
generally  to  rather  large  objects,  plates,  disks,  and  solids  hav- 
ing a  normal  sectional  area  of  one  square  foot  or  more.  For 
small  bodies,  such  as  drops  of  rain  or  even  hailstones,  I  am 
incliued  to  believe  that  Ferrel's  value  of  k  is  nearly  correct, 
that  is  k  =  1.10.  The  uncertainty,  however,  is  such  that  it 
must  be  left  to  the  investigator  to  make  his  choice  as  to  the 
adopted  value.  Consequently  in  Table  56  I  have  kept  the 
value  of  k  apart  from  the  section  containing  the  vertical  veloc- 
ity w.  If  we  choose  for  hailstones  an  average  diameter  of  one 
centimeter,  I  suppose  that  nine-tenths  of  the  value  of  w  given 
in  the  column  under  273  at  the  several  heights  is  about  what 
may  fairly  be  expected  as  the  sustaining  velocity  in  meters  per 
second  up  to  a  height  of  8000  meters.  That  is,  the  value  of  iv 
at  the  freezing  temperature  and  the  height  at  which  hail 
forms  is  as  in  the  following  table: 

TABLE  G5.  —  Probable  sustaining  vertical  velocities,  w,  for  hailstones. 


Probable  sustaining 
velocity. 

Height. 

For 

For  very 

common 

large 

hailstones. 

hailstunes. 

Meters. 

M.  per  s. 

M.  prr  s. 

0 

12.8 

25.6 

1000 

13.6 

27.2 

2000 

14.4 

28.8 

3000 

15.3 

30.6 

4000 

16.2 

32.4 

5000 

17.2 

34.4 

6000 

18.3 

36.6 

7000 

19.3 

38.6 

8000 

20.5 

41.0 

NOVEMBER,  1906. 


MONTHLY  WEATHER  REVIEW. 


511 


STUDIES  ON  THE  THERMODYNAMICS  OF  THE  ATMOS- 
PHERE. 

By  Prof.  FRANK  H.  BIGELOW. 

IX.— THE   METEOROLOGICAL  CONDITIONS   ASSOCIATED   WITH 
THE  COTTAGE  CITY  WATERSPOUT— Continued. 

THE    MAXIMUM    PALLING   VELOCITY    FOB    BAIN    IN     THE     LOWEB 
ATMOSPHEBE. 

The  velocity  in  meters  per  second  which  just  sustains  a  freely 
falling  body  in  the  atmosphere  has  been  computed  by  formula 
37,  Table  56  : 


II.    FOR  COMMON  DROPS,  0.30  to  0.60  mm. 


where  T  is  the  absolute  temperature,  B  the  barometric  pres- 
sure in  centimeters,  D  the  diameter  in  centimeters,  pw  the 
density  of  the  falling  body  in  grams  per  cubic  centimeter, 
and  k  the  so-called  friction  factor,  ranging  from  1.0  to  1.9. 
In  view  of  the  many  combinations  which  can  occur  between 
these  terms,  an  extensive  series  of  tables  would  be  required 
to  express  the  results  in  final  values  of  w,  the  velocity  in  meters 
per  second.  I  have,  therefore,  in  Table  56,  separated  the 
formula  into  its  three  constituent  parts,  for  convenience, 


The  reader  should  select  the  values  that  are  appropriate  for 
the  case  in  hand  and  make  the  necessary  multiplications  in 
order  to  find  the  maximum  falling  velocity.  This  may  be 
properly  illustrated  by  the  example  of  rain,  which  will  require 
some  further  modifications,  because  of  the  facility  with  which 
water  in  the  atmosphere  can  take  on  different  sizes,  since 
drops  occur  ranging  in  diameter  from  0.01  to  7  mm.  In 
the  case  of  rain  /»w=1.0,  and  we  select  £=1.0,  tho  it  will  be 
shown  that  this  is  correct  only  for  common  drops  from 
0.20  to  1.50  mm.  in  diameter.  For  convenience  we  take 


[T 
=  7.503    /    = 

\-B 


15.0  ni.  p.  s.,  since  this  is  the  value  prevailing 


in  the  lower  strata  of  the  atmosphere  at  common  temperatures. 
In  the  Meteorologische  Zeitschrift  for  June,  1904,  Prof.  P. 
Lenard  of  Kiel  has  a  valuable  article  on  rain,  which  will  be 
used  in  this  connection  as  it  affords  some  experimental  data 
of  importance  and  is  generally  in  agreement  with  the  results 
of  the  discussion  already  described  in  the  preceding  pages. 

Table  66,  Bigelow's  formula  for  rain,  contains  the  computa- 

tion for  rainfall,  where  the  drops  are  divided  into  three  classes: 

I.  Diameter,  D=2r,  from  0.01  to  0.20  mm. 

II.  Diameter,  D=2r,  from  0.30  to  0.50  mm. 

in.  Diameter,  D=2  r,  from  1.00  to  5.50  mm. 

Since  the  C.  G.  S.  system  of  units  is  employed  the  values  of 

D=  2  r  must   be    exprest  in   centimeters,    as   in    the    second 

column  ;    the    third    column    contains    v/I)  >   and   the    fourth 

w=  15^/25,  which  is  the  required  velocity  in  meters  per  second. 

TABLE  66.  —  Bigelow's  formula  for  rain. 


w—  7.503 


For  rain  in  lower  atmosphere,  take  p^  :=  1.0  for  water,  and  ft—  1. 


Take  7.503  -  /-=  =  15.0  m.  p.  s.  approximately. 


I.     FOR  FINE  DROPS,  0.01  to  0.20  ram. 


z>.«. 

^5..«V5 

9*r* 

mm.    cm. 

m.  p.  s. 

m.p.s. 

0.  01  =  0.  001 

0.032 

0.48 

0.0032 

0.02  =  0.002 

0.045 

0.67 

0.  0127 

0.  03  =  0.  003 

0.055 

0.83 

0.029 

0.05  =  0.005 

0.071 

1.07 

0.079 

0.10  =  0.010 

0.100 

1.50 

0.32 

0.  20  =  0.  020 

0.142 

2.13 

1.27 

Bmif 

\/l>     w=15  \/  D 

*=£.., 

YP 

mm.        cm. 
0.  30  =  0.  030 

0.173 

m.p.s. 
2.60 

m.p.s. 
2.73 

0.40  =  0.040 

0.200 

3.00 

3.15 

0.  50  =  0.  050 

0.223 

3.35 

3.53 

III.     FOB  LARGE  DKOPS,  i.OO  to  5.50  mm. 


,. 

2r 

Si 

w  =  15   \/  D 

Ob  n. 

1 

k 

mm. 
1.00  = 

cm. 
0.100 

0.316 

4.74 

4.40 

0.98 

.1 

1.50  = 

0.150 

0.387 

5.81 

6.70 

0.94 

.1 

2.00  = 

0.200 

0.447 

6.71 

5.90 

0.88 

.3 

2.50  = 

0.250 

0.500 

7.50 

6.40 

0.85 

.4 

3.  00  = 

0.300 

0.548 

8.22 

6.90 

0.84 

.4 

3.50  = 

0.350 

0.592 

8.88 

7.40 

0.83 

.6 

4.00  = 

0.400 

0.632 

9.48 

7.70 

0.81 

.5 

•  4.  50  = 

0.450 

0.671 

10.07 

8.00 

0.79 

.6 

5.00  = 

0.500 

0.707 

10.61 

8.00 

0.76 

1.8 

5.50  = 

0.550 

0.742 

11.13 

8.00 

0.72 

1.9 

For  fine  drops,  I,  w  ranges  from  0.48  to  2.13. 

For  common  drops,  II,  w  ranges  from  2.60  to  3.35. 

For  large  drops,  III,  w  ranges  from  4.74  to  11.13. 

These  results  are  obtained  by  applying  the  same  law  for  all 
drops,  from  the  finest  to  the  largest  which  occur  in  the  atmos- 
phere. This  must,  however,  be  modified  for  fine  drops,  I,  and 
for  large  drops,  III,  in  order  to  conform  to  the  experimental 
observations.  When  the  drops  are  very  fine  the  viscous 
resistance  of  the  air  becomes  the  prevailing  force  that  holds 
them  from  falling,  and  by  formula  64,  Table  62,  the  maximum 
falling  velocity  is  permanent  for 


9 


By  taking  (/>,„  —  f>)  =  1.00  —  0.00129  =  1.00,  this  becomes 

2  or2 
wm  =  ~~g —  >  which  is  the  formula  employed   by  Lenard  for 

fine  drops.  In  this  g  =  981  cm.,  /t  =  0.0001  2,  by  formula  55, 
Table  62,  and  r  is  taken  in  centimeters.  The  result  in  the 
fifth  column  ranges  for  fine  drops  from  0.0032  to  1.27  m.  p.  s., 
and  they  are  much  smaller  than  those  given  by  the  general 
formula. 

In  the  case  of  common   drops,   Lenard  uses  the  formula 

w2  =  —  r,  where  g  =  981  cm.,  p  =  0.00129,  and  r  =  0.153,  a 

constant  derived  by  experiment.  The  results  range  from  2.73 
to  3.53,  and  are  in  close  agreement  with  the  general  formula, 
where  k  =  1.0.  This  shows  that  the  formula  for  impact  re- 
sistance as  distinguished  from  viscous  resistance  begins  to  be 
applicable  for  drops  whose  diameters  are  about  0.25  mm.  The 
fact  that  k  =  1.0  indicates  that  the  common  drops  do  not  expe- 
rience any  deformation  relatively  to  the  passing  stream  lines, 
the  surface  tension  being  strong  enough  to  simply  adjust  the 
shape  of  the  drop  to  the  curvature  required  for  avoiding  any 
resistance  due  to  the  shape  of  the  body,  except  that  tangential 
to  the  surface  of  the  drops.  When  the  drops  increase  in  size 
beyond  0.50  mm.  a  deformation  sets  in  which  it  is  important 
to  describe  more  fully. 

Professor  Lenard 's  experiments  on  large  drops,  with  diame- 
ters 1.00  to  5.50  mm.,  were  conducted  by  means  of  a  machine 
which  produced  a  vertical  current  whose  velocity  could  be 
regulated  and  measured.  In  the  midst  of  this  the  water  drops 
falling  from  above  were  made  to  float,  and  their  sizes  when  in 
equilibrium  were  studied.  The  resulting  velocities  for  corres- 
ponding diameters  are  given  in  column  5  of  section  III,  and  they 
range  from  4.40  to  8.00  m.  p.  s.  It  was  seldom  that  larger 
drops  than  5.50  mm.  survived  without  breaking  up,  and  the 


512 


MONTHLY  WEATHER  REVIEW. 


NOVEMBER,  1906 


maximum  current  was  8  m.  p.  s.  If  we  divide  this  experi- 
mental value  of  the  vertical  velocity  by  the  computed  velocity 

in  column  4,  we  find  the  ratios «/—  in  column  6,  section  III. 

We  take  out  the  corresponding  values  of  £  which  are 
placed  in  the  last  column  of  Table  66,  where  they  range 
from  1.1  to  1.9.  We  may,  therefore,  render  the  general  for- 
mula for  w  applicable  to  raindrops  of  different  sizes  by 
taking  £=1.0  for  common  drops,  and  gradually  increasing  its 
value  for  large  drops  from  £=1.1  to  £=1.9,  as  indicated  in 
the  table. 

In  his  experiments  on  the  deformation  of  raindrops  in  a 
vertical  current  of  air,  which  could  be  well  observed,  Lenard 
found  that  the  first  effect  of  the  current  on  the  shape  of  the 
drop  was  to  flatten  it  so  that  the  axis  parallel  to  the  direction 
of  the  current  was  shortened.  A  further  increase  of  velocity 
produced  an  increase  of  surface  friction  along  the  meridians 
of  the  drop,  which  also  set  up  oscillations,  and  gradually 
produced  vortex  ring  motion  around  a  circle  in  the  outer 
portion  of  the  drop,  lying  in  a  plane  perpendicular  to  the 
motion  of  the  current.  This  vortex  ring  then  separated 
into  a  corona  of  beads,  the  ring  breaking  up  into  smaller 
drops  which  became  individuals,  and  broke  up  the  large 
drop  into  fine  drops.  The  fine  drops  began  to  increase  in 
size  by  means  of  two  processes,  (1)  collisions  of  drops  in  the 
current,  (2)  the  attraction  of  drops  by  means  of  the  electric 
charges  which  always  accompany  the  aqueous  vapor  in  its 
various  stages  of  ionization.  Lenard  made  counts  for  the 
number  of  drops  of  different  sizes  occurring  in  several  rains 
and  found  that  the  number  of  fine  drops  is  greatly  in  excess 
of  that  for  large  drops.  The  series  of  assorted  sizes  does  not 
change  regularly  from  the  smallest  to  the  largest,  but  they 
accumulate  in  groups,  some  sizes  being  entirely  wanting,  tho 
the  number  of  large  drops  in  any  group  is  not  so  great  as  in 
the  groups  of  small  diameters.  There  is  a  continual  inter- 
change in  the  sizes  and  numbers  in  each  group  because  of  the 
growth,  deformation,  and  separation  of  large  into  small  drops. 
It  is  evident  that  the  true  physical  values  of  the  surface  ten- 
sion in  drops  can  be  obtained  by  computations  on  such  data 
as  that  found  in  this  manner.  In  the  quiet  air  of  the  Tropics 
where  the  aqueous  vapor  content  is  great  the  drops  may  some- 
times grow  to  a  diameter  of  7.0  or  8.0  mm.,  tho  that  is  not 
common.  The  time  of  oscillation  in  the  process  of  deforma- 
tion and  disintegration  is  apparently  two  or  three  seconds. 
The  subject  of  rain  invites  to  more  exact  experimental  re- 
search than  has  yet  been  bestowed  upon  it. 

THE  PROBABLE  VERTICAL  VELOCITY  IN  THE  CLOUD. 

It  is  desirable  to  obtain  some  idea  of  the  vertical  velocity 
within  the  cloud  itself  for  the  purpose  of  judging  of  the 
validity  of  certain  theories  which  have  been  proposed  to  ac- 
count for  the  formation  of  heavy  hailstones.  The  formula  to 
be  employed  is 

w1  =  574.06  -g  A  B, 

in  the  adopted  system  (M.  K.  S.)  where  B  and  J  B  are  in  meters, 
tho,  since  they  occur  in  the  ratio  — =-,  they  can  be  taken  in 

millimeters;  w  is  the  velocity  in  meters  per  second.  Referring 
to  the  data  for  the  waterspout  in  Table  51,  we  find  the  quan- 
tities available  for  the  discussion.  It  is  evident  that  there  is 
no  difficulty  regarding  Tor  B,  but  that  the  value  to  be  assigned 
to  A  B  =  B0  —  B  is  very  uncertain.  At  first  I  take  B0  as  the 
static  pressure  in  the  normal  system  of  gradients  as  obtained 
from  the  Barometry  Report,  and  B  the  pressure  computed 
as  above  from  the  observed  cloud  conditions. 


a-stage. 
(See  Table  51.     Sura'raary  of  data.) 

The  pressure  at  sea  level  is 763.27    mm. 

The  gradient  in  the  static  state  is  — 8.24mm/100m. 

The  height  is  10.78  x  100  meters. 

The  pressure  fall  is — 88.83    mm. 


B0  =  pressure  at  cloud  base  in  static  state  674.44    mm. 
The    gradient   in    the    convection   state    is 

—  8.46  mm/100  m. 
The  pressure  fall  for  10.78  x  100  meters  is —91.20    mm. 


mm. 
mm. 


B  =  pressure  at  the  cloud  base  in    con- 
vection state  (763.27  —  91.20).  .  .    672.07 
(/?„  —  B)a  =  difference  of  pressure  at  cloud  base       2.37 
r=  temperature  (absolute)   at  base  of 

cloud  (273  +  9.3) 282.3° 

wa  =  vertical  velocity  at  the  top  of  the 

a-stage 23.91  m.p.  s 

/J-stage. 

The  gradient  in  the  static  state  is  —  7. 11  mni/100  m. 
The    gradient      in      the     convection    state     is 

—7.40  mm/100  m. 
The  height  is  17.28  x  100  meters. 
(Bt  —  B)ft  =  (7.40—7.11)  x  17.28=0.29x17.28= 
(Bt  —  B)a  =  (8.46-8.24)  X  10.78=0.22 x  10.78= 


5.01 
2.37 


mm. 
mm. 


(B0  —  B)    =  total  change  in  the  pressure 7.38    mm. 

T  =  temperature  at  the  top  of  the  /J-stage  273° 

B  =  pressure  at  the  top  of  the  /9-stage  544     mm. 

WQ  by  the  formula  46.11  m.p.s. 

It  is  seen  from  the  preceding  computation  that  we  have 
found  a  vertical  velocity  of 

wa  =  23.91  meters  per  second  at  the  top  of  the  «-stage,  and 

Wp  =  46.11  meters  per  second  at  the  top  of  the  /J-stage. 

w$  =  small.  The  velocity  is  evidently  small  at  the  top  of 
the  cloud. 

There  are,  however,  a  number  of  reasons  for  thinking  that 
these  large  values  of  w  are  erroneous,  and  must  be  greatly 
diminished.  Since  the  discussion  may  be  of  interest,  altho 
no  satisfactory  decision  is  reached  as  the  result  of  it,  the  fol- 
lowing circumstances  should  be  considered. 

(1)  The  pressures  as  computed  for  the  cloud  levels  have  been 
directly  compared  with    the  static  pressures  as   determined 
from  the  gradients  derived  from  the  Barometry  Report,  and 
therefore  any  error  in  either  of  these  steps  must  be  allowed  for 
in  the  comparison.     It  is  noted  that  while  there  are  no  obvious 
errors  in  the  work,  we  are  yet  dealing  with  small  quantities, 

(B0  —  B)a  =  2.37  mm.  =  0.093  inch,  and 

(B0  —  ff)f  =  5.01  mm.  =  0.197  inch, 

and  that  it  will  require  great  precision  in  the  meteorological 
data  to  make  these  figures  perfectly  reliable. 

(2)  It  has  been  practically  assumed  that  these  two  types  of 
pressure  are  in  action  simultaneously  on  the  same  plane  icithin 
the  cloud  itself.     As  a  matter  of  fact  the  congestive  circula- 
tions producing  a  cumulo-nimbus  cloud  are  very  complex,  and 
they  involve  masses  of  air  outside  the  cloud  limit. 

In  the  case  of  the  Cottage  City  waterspout  the  cold  air  of 
the  anticyclone  flows  over  the  ocean  strata,  and  immediately 
sets  up  a  series  of  currents  of  which  the  cloud  itself  is  one 
effect.  This  indicates  that  the  normal  static  pressure  has 
already  been  disturbed,  and,  therefore,  the  vertical  current 
begins  to  move  before  such  wide  variations  in  (Bo — B)  as  2.37 
or  5.11  mm.  can  occur.  In  fact  the  current  tends  to  fill  up 
the  pressure  difference  as  soon  as  it  begins  to  diverge  from 
the  normal  state,  and  if  it  were  possible  to  trace  this  variation 
exactly,  or  if,  conversely,  we  could  accurately  measure  the 


NOVEMBER,  1906. 


MONTHLY  WEATHER  REVIEW. 


513 


velocity  at  the  several  points,  then  the  problem  could  be  finally 
resolved.  Unfortunately  neither  of  these  measurements  can 
be  made  and  therefore  we  are  limited  to  general  discussions. 
It  is  my  impression,  however,  that  these  facts  indicate  that 
the  pressure  difference  will  seldom  be  as  large  as  1  millimeter 
or  0.040  inch,  which  implies  a  vertical  velocity  of  only  15 
meters  per  second.  There  are  reasons  for  thinking  that  this  is 
the  maximum  value  of  the  vertical  velocity,  and  that  it  seldom  can 
occur  in  nature.  Probably  the  vertical  velocity  is  usually  some- 
thing like  5  meters  per  second  or  even  less,  in  the  midst  of 
such  a  cloud,  but  this  is  merely  an  opinion. 

(3)  It  is  very  probable  that  the  vertical  velocity  increases  to 
a  maximum  within  the  cloud  at  about  the  level  of  the  top  of 
the  j?-stage,  and  that  it  is  small  at  the  top  of  the  cloud,  also 
at  the  sea  level  except  in  the  midst  of  the  vortex.  The  appear- 
ance of  the  cloud,  as  usually  observed,  shows  that  there  is  a 
rapid  vertical  growth  in  the  central  mass  from  the  base 
upward,  and  that  a  sort  of  boiling  with  overflow  to  the  sides 
takes  place,  except  as  disturbed  by  penetrating  into  other 
moving  strata.  Since  several  theories  of  hail  formation  depend 
upon  a  very  strong  vertical  current,  it  has  been  important  to 
point  out  the  fact  that  the  vertical  velocity  does  not  probably 
exceed  15  meters  per  second,  and  that  evidence  implies  that  this 
is  generally  too  high.  We  will  consider  briefly  the  theories 
proposed  for  the  formation  of  large  hailstones,  and  then  make 
such  suggestions  as  seem  warranted  by  the  conditions  deter- 
mined in  this  special  cloud. 

APPROXIMATE  POSITION  OF  THE  ISOTHERMS  AND  ISOBARS  IN  THE  COTTAGE 
CITY   WATERSPOUT    CLOUD. 

The  practical  difficulty  of  solving  this  problem  lies  in  the 
fact  that  the  data  are  wanting  with  which  to  compute  the 
value  of  A  B  in  the  formula, 

6~AB. 
B 

It  is  important  to  approach  the  true  value  at  least  approxi- 
mately, if  possible,  and  for  that  purpose  I  have  made  the  fol- 
lowing trial  computations,  shown  in  Table  67.  The  data  for 
the  B,  t,  R.H.  as  selected  for  the  three  hours,  4  p.  m.,  1  p.  m., 
and  10  a.  m.,  are  indicated  in  English  measures,  and  trans- 
formed into  metric  measures.  The  mean  temperatures,  0,  of 
the  air  column  in  the  a,  /?,  ?-,  a  stages  are  determined  as  fol- 
lows: Plot  the  values  of  t,  58°,  67.5°  and  65°  on  the  sea  level; 
compute  from  the  gradients  of  Table  51,  summary  of  data,  the 
heights  at  which  58°  and  65°  occur  over  the  1  p.  m.  and  10  a.  m. 
columns,  and  draw  the  isotherms;  plot  the  temperature  48.7° 
at  the  height  of  the  bottom  of  the  ,9-stage,  32°  at  bottom  and 
top  of  the  f-stage,  and  10.4°  at  top  of  the  cloud,  as  indi- 
cated on  fig.  39.  Then,  I  have  drawn  the  isothermal  slopes 
by  judgment,  admitting  that  they  may  need  modification  to 
be  true  to  nature,  tho  there  is  no  criterion  now  available.  The 
temperature  was  determined  at  each  500-foot  level  in  the  three 
columns,  and  for  the  intermediate  250-foot  points  by  taking 
the  means  of  successive  pairs  of  values.  This  gives  6  pairs  in 
the  a-stage,  12  in  the  /3-stage,  and  13  in  the  <5-stage.  The 
mean  of  the  several  a,  /5,  y,  ''  groups  gives  the  values  of  8 
for  the  several  stages  as  shown  in  Table  67.  The  values 
of  the  vapor  tension,  e,  were  computed,  taking  the  relative 
humidity,  R.  H.,  given  for  the  a-stage,  and  100  per  cent  in  the 
other  stages.  They  may  not  be  exactly  correct,  but  they  are 
sufficient  for  a  close  barometric  reduction  by  the  formula, 

log  B  =  log  Bo  —  m  +  jim  +  fni, 

the  -fm  term  being  negligible  in  the  latitude  of  Cottage  City. 
For  the  purpose  of  comparing  the  resulting  pressures  for 
the  several  stages  found  by  the  static  formula  just  given  and 
those  found  by  the  thermodynamic  formulas  as  given  in  Table 
51,  summary  of  data,  we  select  for  1  p.  m.  the  following 
figures: 


Stages.          Static  method. 


(top) 


(bottom) 


414.56 
539.02 
544.02 
672.30 
763.27 


Thermodynamic 
method. 

m  m. 
414.50 
539.00 
544.00 
672.00 
763.27 


This  shows  that  these  two  groups  of  formulas  and  the  de- 
pendent tables  work  together  in  entire  harmony,  considering 
the  very  different  ways  of  using  the  temperature  terms,  since 
they  are  involved  by  means  of  their  diverse  functions.  The 
resulting  isobars  for  the  stages  are  indicated  on  fig.  39,  as- 
sumed approximate  position  of  the  isotherms  and  isobars.  It 
is  noted  that  from  the  beginning  to  the  end  of  the  disturbance, 
from  10  a.  m.  to  4  p.  m.,  the  isobars  in  the  cloud  region  change 
by  about  1  mm.  of  mercury.  In  the  immediate  neighborhood 
of  the  waterspout,  1  p.  m.,  there  may  have  been  a  series  of 
abrupt  rises  and  falls  of  the  pressure,  such  as  are  usually 
found  on  the  barograph  traces  in  thunderstorms;  the  extent 
of  these  I  can  not  determine  for  this  case,  but  the  important 
fact  is  that  the  range  of  J  B  must  have  been  about  1  mm.  in 
the  cloud,  because  it  is  hardly  probable  that  it  should  have 
exceeded  for  any  short  interval  the  total  change  between  the 
10  a.  m.  and  4  p.  m.  extremes.  By  entering  1  mm.  in  the  for- 
mula, we  find 

w  =  15.52  meters  per  second. 


of 


J6000 


/2OOO 


//OOP 


fooo 


8000 


6000 


3000 


'/OOP 


zaoo 


of  vouch* 


neters 


Z880 


30 


/5 


30 


ZO" 


FIG.  39.— Approximate  position  of  isotherms  and  isobars. 

This  agrees  with  my  previous  estimate  of  the  vertical  veloc- 
ity. It  is  evident  that  in  the  other  computation,  where  the 
mean  gradient  for  the  month  was  used,  as  derived  from  the 
Barometry  Report,  namely,  —8.24  for  the  a-stage  and  — 7.11 
for  the  /S-stage,  Table  51,  we  assumed  that  the  conditions  for 
the  waterspout  were  the  same  as  those  of  the  mean  of  August 


514 


MONTHLY  WEATHER  REVIEW. 

TABLE  Gl.— Computation  of  the  isobars  at  three  hours,  August  19,  1S96. 


NOVEMBER,  1906 


4  p.  m. 

1  p.  m. 

10 

a.  m. 

5=30.10 
<=58.0° 
R.  5=60% 
#a=51.4F. 
00=36.7  P. 
#a  =19.5F. 

=  764.54  mm. 
=   14.44  C. 
e=   7.33  mm. 
=  10.78  C. 
=   2.61  C. 
=  -6.94C. 

5=30.05 
<=67.5° 
JR.  H.  =  64% 
#a=58.8F. 
#p=39.9F. 
#{  =21.5F 

=  763.27  mm. 
=   19.72  C. 
e=   10.92  mm. 
=  14.89  C. 
=  4.39  C. 
=  —  5.8  S  C. 

5=30.03    = 
t=65.Q°    = 
/?.//.  =  67% 
0a=57.0F.  = 
0ft  =41.7  F.  = 
#4  =23.9F.  = 

762.76  mm. 
18.33  C. 
e=  10.49  mm. 
13.89  C. 
5.39  C. 
—4.50  C. 

(a)  5=  1078 
#=10.78 
e=  7.33 

log  50=  2.88340 
m  =—  .05625 
/3m  =+          18 

5=  1078 
#=14.89 
e=10.92 

log  Ba=  2.88268 
m  =—  .05546 
/3m  =+          28 

5=  1078 
#=13.89 
e=10.49 

log  /;„=  2.88239 
m  =—  .05561 

/3m  =+          26 

log  5=2.82733 
B=  671.94 

log  5=2.82750 
B=  672.30 

log  5=2.82704 
5=   671.49 

(/3)  5=  1728 
6=  2.61 
<=  7.22 

o          7  KB 

log  50=  2.82733 
m  =  —  .09286 
/3m=  +          32 

H=  1728 
8=  4.39 
<=   9.44 

c        H  HO 

log  50=  2.82750 
m  =  —  .09226 
/3m  =+          38 

H=  1728 
#=   5.39 
«—  10.17 

p        q  94. 

log  #0=2.82704 
m   =  -  .09193 
ftm  =  +          39 

log  £  =2.73479 
B=  542.99 

log  B  =2.73562 
B=  544.02 

log  5  =2.73550 
5=   543.88 

(r)  5=74 

J  5=  —  5.00 
5=  537.99 

A  B=  -  5.00 
5=   539.02 

.  J  5=  —  5.00 

5=   538.88 

(.5)5  =  2062 
6=—  6.94 
e=4.57 

log  50=2.73077 
m  =  —  .11477 
/3m  =  +          28 

5=2062 
#=5.83 
e=4.57 

log  50  =2.73161 
m    =  —  .11430 

/3m  =  +          28 

5=2062 
#=—4.50 
e=4.57 

log  5.  =2.73149 
m  =  -  .11373 

/3m  =+          28 

log  B=  2.61628 
B=  413.31 

log  5=2.61759 
5=  414.56 

log  5=2.61804 
5=  414.99 

taken  day  and  night.  But  the  waterspout  occurred  at  midday, 
and  the  gradient  was  probably  nearer  the  adiabatic  rate,  — 8.46 
for  the  a-stage  and  — 7.40  for  the  /3-stage,  than  was  supposed. 
The  practical  difficulty  of  successfully  treating  this  part  of  the 
discussion  is  a  great  barrier  to  concluding  the  analysis  of  the 
dynamic  conditions  as  derived  from  the  thermodynamic  state 
of  the  cloud,  and  additional  observational  data  are  much 
needed  under  similar  thunderstorm  actions.  Finally,  I  adopt 
as  the  most  probable  maximum  velocity  of  the  vertical  current 

w  =  15  meters  per  second. 

THE    BUILDING    OF    HAIL. 

The  literature  of  the  discussion  of  the  many  problems  con- 
nected with  the  making  of  hailstones  in  the  air  is  very  exten- 
sive, but  the  following  references  are  sufficient  to  place  the 
subject  before  the  reader  in  its  most  recent  phases: 

Recent  Advances  in  Meteorology,  William  Ferrel.  Appendix 
71,  Annual  Report  of  the  Chief  Signal  Officer  for  1885,  Part  2. 
Pp.  302-315. 

Lehrbuch  der  Meteorologie,  J.  Hann.     1901.     Pp.  682-699. 

Die  Bildung  des  Hagels,  Wilh.  Trabert,  Meteorol.  Zeitschr., 
October,  1899.  Pp.  433-447. 


Beitrage  zur  Hageltheorie,  P.  Schreiber.  Meteorol.  Zeitschr., 
February,  1901.  Pp.  58-70. 

Hailstones,  F.  W.  Very.  Transactions  of  the  Academy  of 
Science  and  Art,  Pitts  burg;  lecture  January  5,  1904. 

Doctor  Trabert's  paper  contains  many  references  to  other 
papers  on  hail. 

The  physical  structure  of  hailstones  is  about  as  follows: 

1.  Central  nucleus  of  opaque  snow  or  snowy  ice,  consisting  of 
snowflakes  and  ice  crystals  mixed  with  air  bubbles  from  0.1  to 
0.5  inch  in  diameter. 

2.  Layer  of  clear  ice,  or  pellucid  material  containing  incisted 
air  cells  and  liquid  in  radiating  inclosures.     It  is  0.1  to  0.2 
inch    thick   and   terminates   in   a   sharply   defined   spherical 
boundary,  or  else  in  a  more   irregular  boundary   to   which 
adhere  mammillary  masses  of  soft  snow,  which  may  be  0.1 
inch  in  thickness.     The  clear  layer  itself  is  built  up  of  a  col- 
lection of  many  small  drops,  which  are  instantly  stiffened,  as 
in  undercooled  water,  which  is  5°  to  10°  below  the  freezing 
temperature,  when  water  falls  below  zero  without  freezing 
and  then  sets  with  a  shock.     The  ice  crystals  are  mixed  in  a 
motley  array. 

3.  A  series  of  opaque  and  clear  layers  succeed  each  other,  as 


NOVEMBER,  1906. 


MONTHLY  WEATHER  REVIEW. 


515 


many  as  fourteen  having  been  counted,  the  last  layer  usually 
being  opaque  and  adhering  to  a  very  thin  layer  of  clear  ice. 

The  diameters  of  hailstones  vary  from  0.5  inch  to  4  inches; 
a  frequent  size  is  1  inch  to  2  inches.  The  shapes  of  hailstones 
may  be  divided  into  two  classes:  (1)  Those  which  have  a  thick 
base  and  pointed  top,  such  as  conical  with  a  flat  base,  pyramidal 
with  a  round  base,  pear  shape  with  a  concave  base,  and  mush- 
room shape  with  the  table  downward.  In  these  the  accretions 
are  chiefly  on  the  lower  side  of  the  body,  as  if  gained  in  falling 
thru  layers  of  snow  and  water  drops  to  the  ground.  (2)  Those 
which  are  regularly  disposed  about  a  center,  as  if  they  grew 
regularly  from  all  sides,  and  are  spherical,  ellipsoidal,  lens- 
form  and  hemispherical,  the  ellipsoidal  being  most  common. 
The  stones  frequently  indicate  some  effects  as  from  a  rotary 
motion  about  an  axis,  so  that  they  grow  in  a  certain  plane 
more  readily  than  in  other  places.  The  clear  ice  forms  chiefly 
on  the  large  plane  like  a  tooth-shaped  disk,  the  forms  being 
many  and  irregular,  depending  on  the  accumulation  of  hex- 
agonal ice  crystals. 

The  order  of  construction  from  the  center  outward,  if  there 
were  no  repetition  of  the  layers,  would  probably  be: 

1.  Center  =  snow  belonging  to  the  5-stage  in  the  cloud. 

2.  Snow  and  ice  mixed  =  the  undercooled  crystals  of  the 


3.  Clear  ice  =  the  gradual  cooling  ice  of  the  /?-stage  in  con- 
tact with  a  cold  nucleus. 

If  there  are  repetitions,  it  follows  that  these  stages  are  mixt  in 
the  internal  circulation  of  the  cloud,  and  that  they  are  brought  in 
contact  with  the  nucleus  in  succession  by  falling,  or  by  some  other 
mechanical  process.  The  undercooling  of  the  f-stage  and 
'J-stage  must  be  due  to  sudden  transitions  of  the  stone  from 
one  layer  to  another  having  different  temperatures.  The 
gradual  cooling  must  be  due  to  the  contact  of  saturated  water 
drops  in  the  ;?-stage  with  the  nucleus  which  has  passed  out 
of  the  5-stage  and  the  ?--stage  into  the  /5-stage.  The  irregu- 
larities merely  record  the  congested  state  of  the  air  and  a 
mixt  condition  of  the  <5-?--/?-stages. 

Hailstones  are  usually  of  aboiit  one  kind  in  the  same  storm, 
but  they  change  their  type  from  storm  to  storm.  Hail  is 
formed  at  the  rear  of  the  rising  column  of  warm  air,  at  the 
place  of  marked  changes  in  the  isotherms,  when  the  barometer 
is  beginning  to  rise  rapidly  and  the  wind  shifts  from  the  south 
to  the  northwest.  This  is  the  locus  of  the  contact  of  two  counter 
currents  of  air  having  very  different  temperatures,  and  hail  forma- 
tion is  one  of  the  results  of  the  rapid  progress  of  the  warm  and  cold 
layer*  toward  thermal  equilibrium.  The  energy  difference,  which 
marks  the  departure  from  the  normal  equilibrium,  does  not 
lie  in  a  vertical  direction  so  much  as  in  a  horizontal  direction. 
There  is  a  rapid  rise  of  warm  air  with  condensation  of  the 
vapor,  as  in  a  thunderstorm,  and  the  lightning  usually  occurs 
at  about  the  time  of  hailfall,  but  it  is  sometimes  earlier  and 
at  other  times  later,  and  not  necessarily  simultaneous.  On 
mountains  it  is  said  that  there  is  always  lightning  with  hail 
and  in  the  valleys  sometimes  lightning  with  hail.  On  moun- 
tains there  are  observed  to  occur  simultaneously  lightning, 
undercooled  drops,  and  snow  crystals.  In  falling  thru  the 
warm  «-stage  the  outer  opaque  coating  of  the  hailstone 
becomes  covered  with  liquid  water  and  in  this  condition  the 
stone  falls  to  the  ground. 

THEORIES    OF    THE    FORMATION    OF    HAILSTONES. 

There  are  many  theories  regarding  the  mode  of  formation 
of  hailstones,  in  each  of  which  there  is  probably  an  element  of 
truth.  None  of  them  can  be  said  to  be  entirely  satisfactory, 
and  yet  it  is  very  likely  that  nearly  all  of  the  assigned  natural 
causes  and  effects  generally  operate  in  producing  the  phenom- 
ena. The  two  principal  facts  to  be  accounted  for  are,  (1)  the 
presence  of  the  cold  which  causes  the  sudden  stiffening  of  the 
water  drop  at  undercooled  temperatures,  and  (2)  the  alterna- 


tion of  snow  and  water  materials  in  the  successive  layers.  In 
the  sudden  cooling  of  the  water  drops  there  is  evolved  a  con- 
siderable amount  of  latent  heat,  and  the  cold  must  be  present 
to  such  an  extent  as  to  overcome  the  restraining  effect  of  this 
latent  heat,  and  yet  produce  cooling  as  by  a  shock  of  the 
molecular  material  in  the  water.  The  theories  may  be  briefly 
summarized  as  follows: 

1.  The  oscillation  theory. — It  is  assumed  that  two  cloud  layers 
of  different  temperatures  are  superposed,  and  that  a  hailstone 
oscillates  up  and  down   between    them    under   an    electrical 
attraction  and  repulsion,  one  cloud  being  charged  with  nega- 
tive electricity,  and  the  other  with  positive  electricity.     This 
theory  is  now  considered  unnatural  and  arbitrary,  and  it  cer- 
tainly is  not  true,  because  no  electrical  forces  exist  in  clouds 
capable  of  thus  moving  heavy  stones  up  and  down  in  the 
presence  of  gravity. 

2.  The  orbital  theory. — Professor  Ferrel  postulated  a  verti- 
cal orbit  in  the  cloud,  in  connection  with  an  internal  vortex 
tube  having  a  vertical  axis,  and   supposed   that   the    stones 
past  around  this  thru  considerable  changes  in  altitude,  and 
thru  masses  of  different  structure.     Such  a  flow  of  air  inside 
the  cloud  is  very  improbable,  and  there  is  no  evidence  that 
the  cloud  thus  rotates.     A  modification  of  this  view  is  found 
in  the  horizontal  roll  which  very  frequently  exists  on  the  back 
side  of  the  warm  ascending  current,  at  the  place  of  the  most 
active  mixing  with  the  cold  column.     It   is  very  likely  that 
this  does  often  develop  in  thunderstorm  clouds,  and  indeed, 
there  may  be  several  such  rolls  on  horizontal  axes,  and  their 
action  may  well  produce  certain  effects  upon  the  construction 
of  hailstones  of   different  types;  the  effects  are  confined  to 
merely  differential  variations  of  the  typical  structures.     The 
vertical  component  can  hardly  lift  the  stones,  except  those  of 
the  smaller  sizes.     If  the  upward  current  on  one  side  retards 
a  freely  falling  stone,  on  the  other  side  of  the  roll  it  would 
accelerate  its  fall,  and  so  discharge  it  from  the  local  action  in 
the  cloud  by  this  impulse. 

3.  The  upward  current  theory. — The  sustaining  force  of  a  strong 
upward  current  of  air  in  the  midst  of  the  cloud,  whereby  a 
hailstone  is  held  aloft  for  a  considerable  time  while  it  receives 
accretions  from  the  contents  of  the  ascending  stream,  acting 
especially  on  the  under  side,  is,  doubtless,  the  most  important 
theory  to  be  examined.    The  growth  on  the  underside  of  a  hail- 
stone can  be  accounted  for  either  by  falling  from  a  consider- 
able height  thru  the  cloud,  or  by  being  sustained  at  a  given 
height  by  an  upward  flowing  current.     There  are  several  diffi- 
culties if  not  objections  to  this  theory,  when  taken  as  the  single 
cause  of  the  formation. 

(1)  The  condensation  products  carried  in  the  vertical  current 
do  not  seem  sufficient  to  produce  the  largest  stones. 
Let  W  =  grams  of  water  in  1  cu.  meter. 

W 
™  =  grams  of  water  in  1  cu.  centimeter. 

A   stone  of  section   nr*  falling    thru  a  height  dh  will   gain 
W 


10" 


.  -r'  .  dh   grams,  which  is  equal  to  a  volume  increase   of 


4  Trr2 .  dr.     Hence,  dr= 


W 
4xTO~6 


dh,  and  r}  —  rl  = 


W 


4  000  000 


(ht  —  h,).  If  the  height  of  fall  is  2  kilometers  (200,000  cm.), 
and  W==  4  grams,  at  freezing  temperatures,  then  J  r  =  0.2 
cm.  =  2  mm.  This  is  Trabert's  argument,  and  he  thinks  it  does 
not  fully  account  for  the  large  stones  which  are  found 
weighing  as  much  as  250  to  1000  grams.  This  view  conceives 
the  stones  to  form  in  the  3  and  ?--stage  as  ordinarily  stratified 
in  a  quiet  cloud,  but  I  think  that  suitable  modification  can  be 
indicated,  which  will  to  some  extent  avoid  the  difficulty. 

(2)  The  stream  lines  around  the  stone  will  doubtless  carry 
off  some  of  the  particles  of  water  without  their  touching  the 


516 


MONTHLY  WEATHER  REVIEW. 


NOVEMBER,  1906 


stone  itself,  and  this  will  tend  to  diminish  the  quantity  that  is 
actually  deposited,  thus  strengthening  the  former  objection 
that  the  total  quantity  of  deposit  is  insufficient  to  produce  the 
mass  of  the  observed  hailstones. 

(3)  It  is  not  easy  to  account  for  the  concentric  layers  on  the 
upward  current  theory,  or  the  downward  fall  theory  in  a  simple 
cloud. 

(4)  In  seeking  to  maintain  this  current  theory  of  accretion, 
Professor  -Schreiber,  it  seems  to  me,  has  assumed  excessive 
heights  and  improbable  velocities  in  the  ascending  currents. 
Thus,  he  makes  two  assumptions:  (a)  that  the  vertical  velocity 
increases  steadily,  at  the  rate  of  3  meters  per  second  per  1000 
meters  of  altitude,  as  in  the  second  column  of  the  following 
table;  (6)  that  the  vertical  velocity  increases  at  the  rate  of  7.5 
meters  per  second  per  1000  meters,  up  to  20,000  meters  of 
altitude,  and  then  diminishes  at  the  same  rate,  down  to  0  at 
40,000  meters,  as  in  the  third  column  of  the  following  table. 

Schreiber'a  assumed  vertical  velocities. 


Height  in 
meters. 

(«) 

(») 

30000 

m.  p.  s. 
90 

m.  p.  s. 
78 

20000                    

60 

150 

10000  

30 

75 

5000 

15 

37  5 

4000     

12 

30.0 

3000 

9 

22.5 

2000                  

6 

15.0 

1000 

3 

7  5 

0  .              ..   .. 

0 

0 

He  makes  two  other  assumptions  for  trial,  (1)  that  the  vertical 
current  has  no  limit  in  height,  and  the  same  velocity  and 
density  thruout,  and  (2)  that  the  velocity  is  the  same  thruout, 
but  that  the  density  diminishes  with  the  height.  He  dis- 
cusses the  sorting  velocities  which  separate  the  stones  of  dif- 
ferent diameters,  those  larger  than  the  critical  velocity  falling 
to  the  ground,  and  those  smaller  rising  in  the  current  and 
growing  to  larger  size  in  preparation  for  a  fall.  It  may  be 
remarked,  generally,  that  cloud  heights  above  10,000  meters 
are  rarely  measured,  and  that  the  vertical  velocities  are  a 
maximum  within  the  cloud,  probably  at  the  height  of  the 
p-stage,  rather  than  at  the  top,  somewhat  as  assumed  in  his 
fourth  trial  (p.  62),  but  by  no  means  at  such  large  values  of 
the  current.  Schreiber  asserts  that  hail  forms  at  the  top  of 
such  lofty  clouds  as  30,000  meters  and  in  vertical  currents  of 
100  meters  per  second,  which  it  seems  to  me  is  impossible  in 
view  of  the  fact  that  such  clouds  do  not  exist,  and  that  by 
adiabatic  laws  the  ^-stage  is  seldom  higher  than  6000  meters 
in  the  most  favorable  summer  conditions.  In  this  connection 
refer  to  my  discussion  of  the  heights  of  the  several  stages, 
Cloud  Report,  Annual  Report  Weather  Bureau,  1898-1899, 
pages  720-723,  and  chart  74.  There  can  be  little  doubt  that 
we  must  confine  the  formation  of  hail  to  the  region  3000-7000 
meters  above  the  ground,  and  usually  to  the  middle  height, 
most  frequently  near  the  5000-meter  level.  It  is  noted  that 
Schreiber  assigns  a  vertical  velocity  of  15  m.  p.  s.  at  the 
5000-meter  level,  and  that  this  agrees  with  the  maximum  ver- 
tical velocity  which  it  seems  probable  can  be  developed  in  an 
ordinary  summer  cloud.  This  is  not  strong  enough  to  sustain 
a  hailstone  of  1  cm.  diameter,  which  is  a  small  specimen,  as  a 
velocity  of  20  m.  p.  s.  is  required  for  that  purpose,  while 
40  m.  p.  s.  is  required  to  sustain  a  large  stone  4  cm.  in 
diameter. 

4.  The  electrical  attraction  theory. — In  order  to  escape  from 
such  difficulties  as  those  just  enumerated  in  the  vertical  cur- 
rent theory,  Trabert  advocates  the  theory  that  the  sudden 
accumulation  of  drops  on  the  nucleus  at  undercooled  tem- 
peratures is  due  to  the  electrical  charging  of  the  nuclei  at  the 
instant  of  a  lightning  flash,  the  surface  charges  having  the 


power  to  attract  water  drops  to  the  charged  surface.  The 
drops  of  a  jet  of  water  are  thus  suddenly  drawn  together  by 
an  electrified  piece  of  wax  placed  near  it.  The  drops  fly 
together  when  changes  take  place  in  the  electric  field  sur- 
rounding them.  Some  observers  say  that  there  is  no  hail 
without  the  electric  phenomena.  Each  layer  of  ice  is  made 
suddenly  by  electric  impulses  which  follow  in  succession  for 
the  several  layers.  The  deposit  of  a  layer  brings  the  under- 
cooled  temperature  up  to  the  freezing  point.  The  escaping 
heat  of  the  undercooled  mass  in  condensing  makes  a  water 
layer  on  the  outside  which  changes  to  ice.  There  is  a  con- 
siderable quantity  of  latent  heat  evolved  in  the  process  of 
water  and  ice  formation.  Hail  weather  and  lightning  weather 
are  alike  in  kind  and  different  in  intensity.  Thunderstorms 
are  associated  with  the  horizontal  roll  due  to  overturning,  and 
hailstones  with  the  vertical  vortex  due  to  excessive  convection 
currents.  It  has  been  suggested  that  the  heat  of  the  convec- 
tion process  is  transformed  into  electricity  and  that  the  required 
cooling  is  produced  in  that  way,  but  of  this  there  is  little  evi- 
dence. The  cooling  is  also  referred  to  sudden  expansion  in 
the  air,  but  this  would  produce  so  great  changes  in  the  ba- 
rometer that  it  would  be  readily  detected. 

This  electrical  theory  ought  to  play  a  part  in  the  formation 
of  hail  at  times,  but  it  is  hardly  demonstrable  that  hail  does 
not  fall  without  lightning,  and  certainly  it  is  not  shown  that 
a  flash  of  lightning  occurs  at  the  time  of  the  deposit  of  the 
several  stratified  layers.  A  hailstorm  often  lasts  many  minutes, 
and  during  that  time  there  must  be,  on  this  theory,  such  an 
incessant  recurrence  of  lightning  to  match  the  numerous  lay- 
ers of  ice  that  it  would  be  a  very  conspicuous  event.  There 
are  many  instances  known  in  which  the  lightning  seems  to 
have  really  followed  the  hail  by  many  seconds,  but  it  should 
evidently  precede  it,  if  the  time  allowance  for  the  fall  from 
the  cloud  to  the  ground  is  subtracted  from  the  instant  when 
the  hail  is  seen  to  fall  upon  the  ground.  F.  W.  Very  writes: 

Severe  hailstorms  are  almost  universally  accompanied  by  thunder 
and  lightning,  but  the  electrical  display  is  apt  to  lag,  and  even  to  attain 
Its  greatest  development  as  the  storm  advances  to  its  close. 

The  rising  air  carries  up  the  low  surface  potential  on  the 
front  side  of  the  hail  squall,  and  the  descending  air  brings 
down  the  high  potential  of  the  upper  levels,  so  that  there  is 
an  increase  in  the  difference  of  potential  at  the  hail  level 
which  causes  horizontal  flashes  in  the  cloud,  for  the  greater 
part.  The  earth's  negative  charge  is  carried  aloft  to  the  hail- 
stones, which  are  often  negatively  charged.  Snow  which  forms 
in  the  high  levels  is  usually  positively  charged.  Reversals  of 
the  ordinary  disposition  of  the  electric  potential  have  been 
noted  as  the  effect  of  snow,  hail,  and  water  inductions  brought 
to  the  surface  of  the  ground. 

5.  The  stratification  theory. — After  the  foregoing  examination 
of  the  theories  that  have  been  heretofore  proposed  for  the  ex- 
planation of  the  growth  of  hailstones,  I  proceed  to  examine 
the  subject  from  a  new  point  of  view,  which  seems  to  me  to 
offer  certain  advantages  over  the  other  theories,  and  to  em- 
body the  best  points  of  them  all.  This  I  call  the  stratification 
theory.  It  happens  that  a  hailstorm  cloud,  which  is  merely 
an  intense  form  of  thunderstorm  cloud,  really  consists  of  two 
component  portions  separated  from  each  other  by  isothermal 
surfaces  inclined  forward  from  the  vertical.  On  the  front  side 
the  air  is  much  warmer  than  on  the  back  side,  and  along  the 
line  of  separation  the  contour  is  strongly  stratified  by  the 
mutual  interpenetration  from  opposite  directions  of  layers 
having  different  temperatures. 

Fig.  40,  "  Stratification  of  the  /?  and  '5-stages  in  a  thunder- 
storm cloud  with  hail ",  roughly  illustrates  the  idea.  Such 
storms  begin  in  consequence  of  the  transportation  of  cold  air 
into  a  region  of  warm  air,  and  in  many  cases  the  difference  of 
temperature  amounts  to  as  much  as  20°  F.  The  tendency  for 


NOVEMBER,  1906. 


MONTHLY-jWEATHEE  REVIEW. 


517 


such  masses  of  air  at  different  temperatures  is  to  mix  inti- 
mately and  irregularly  in  order  to  restore  the  thermal  equili- 
brium as  rapidly  as  possible.  The  cold  air  is  carried  forward 
in  the  high  levels,  and  like  a  sheet  overflows  the  warmer  lower 
layers,  as  is  indicated  by  the  first  formation  of  clouds  of  the 
cirrus  type,  which  later  change  into  alto-cumulus  and  alto- 
stratus  types. 


FIG.  40.— Stratification  of  ,3-  and  J-stage  in  a  cloud  with  hail. 

The  body  of  warm  air  tends  to  rise  and  interpenetrate  the 
cold  air  in  a  congested  circulation  including  numerous  minor 
whirls  and  small  vortices.  On  the  western  side  of  the  column 
of  rising  warm  air  the  tendency  to  stratification  of  the  warm 
and  cold  layers  in  horizontal  directions  is  very  pronounced, 
the  sheets  of  different  temperatures  penetrating  strongly  at  a 
series  of  intervals  in  elevation,  so  that  they  lie  over  each  other 
on  a  given  vertical  in  succession  which  may  be  repeated  many 
times.  The  boundary  between  the  ,3-stage  and  the  <S-stage,  or 
the  course  of  the  ^-stage,  is  therefore  folded  upon  itself  sev- 
eral times  in  a  vertical  direction. 

For  example  we  may  suppose  that  the  temperatures  are 
arranged  in  some  such  manner  as  the  following: 


Let/5=  +  15° 
let  ,3  =  +  10° 
let  /?=  +  5° 
let  ,?=  +  0° 

The  temperatures 
in  the  '5- stage,  and 
with  the  height. 

The  snow  nucleus 
water  carried  aloft 


C.  and  S  =  —  2°  C.  in  the  lowest  fold; 
C.  and  S  =  —  4°  C.  in  the  second  fold ; 
C.  and  <S  =  —  6°  C.  in  the  third  fold; 
C.  and  S  =  —  8°  C.  in  the  fourth  fold; 


in  the  /J-stage  fall  off  more  rapidly  than 
the  difference  between  them  diminishes 

,  starting  from  a  great  height,  meets  the 
in  the  warm  strata,  is  coated  with  the 


drops,  which  are  chilled  by  its  lower  temperature  and  frozen  in 
irregular  semicrystaline  forms.  The  vertical  current  at  even 
moderate  velocities  is  able  to  carry  up  all  the  water  contents 
in  the  form  of  drops,  and  they  are  injected  as  it  were  sideways 
from  a  fountain  into  the  higher  strata.  The  snow  nucleus  is 
therefore  simply  exposed  to  a  spray  of  water  drops,  brought 
from  the  lower  strata  where  high  vapor  contents  prevail, 
because  of  the  warm  air  occupying  the  lower  levels  before 
they  were  disturbed  by  the  overflowing  anticyclonic  cold. 
The  cold  nucleus,  therefore,  suddenly  condenses  a  layer  of 
clear  ice,  or  ice  and  snow  when  mixt  by  the  minor  vortices 
and  horizontal  rolling  of  the  air.  The  small  hailstone  then 
falls  by  gravity  thru  successive  stratifications  of  the  snow  and 
rain  stages,  it  grows  on  the  underside  by  special  accumula- 
tions there,  and  finally  reaches  the  ground,  having  received 
as  many  layers  as  there  are  distinct  horizontal  minor  stratifi- 
cations. The  undercooling  takes  place  chiefly  in  the  highest 
stratifications,  and  ice  or  snow  crystals  are  found  deposited  in 
the  inner  layers  of  the  hailstone.  The  under  cooling  dimin- 
ishes with  the  descent  so  that  the  outer  layers  are  watery  or 
simply  opaque. 

There  evidently  exists  a  series  of  small  horizontal  rolls  pro- 
duced by  the  dynamic  action  of  the  interflowing  sheets,  where 
the  mixture  of  air  at  different  temperatures  is  facilitated  by 
drawing  it  out  into  thin  ribbons,  as  in  ordinary  cyclonic  cir- 
culations. The  lowest  cold  stratum  flows  forward  on  the 
ground,  producing  the  squall  of  cold  air  that  precedes  the 
rainfall.  An  examination  of  the  isotherms  and  isobars  on 
fig.  39  shows  that  this  distribution  of  the  air  currents  is  the 
probable  one,  allowing  for  the  minor  configurations  on  the 
edges  of  the  mixing  masses.  The  isobars  show  that  at  the 
sea  level  the  air  flows  forward,  but  in  the  upper  levels  it  flows 
backward  at  the  time  of  the  hailstorm.  The  isotherms  show 
that  there  is  an  excess  of  upward  velocity  at  the  line  of  separa- 
tion, and  also  that  the  flow  is  backward  in  the  higher  levels. 
The  production  of  lightning  discharges  under  these  condi- 
tions, especially  in  the  region  where  the  cloud  is  serrated  as 
to  temperatures,  is  evidently  to  be  anticipated,  in  consequence 
of  the  rapid  changes  occurring  in  the  thermal  conditions  and 
the  water  contents.  The  hailstones  may  therefore  be  heavily 
charged  with  positive  electricity,  or  even  with  negative  elec- 
tricity, under  these  circumstances,  and  the  fallen  hailstones 
may  exhibit  electrical  states  by  no  means  uniform  from  storm 
to  storm. 

It  is  desirable  that  numerous  computations  be  made  on  the 
data  that  may  be  obtained  from  the  surface  observations  in 
thunderstorms  and  in  hailstorms,  with  the  view  of  transform- 
ing our  inferences  regarding  the  thermal  operations  going  on 
in  the  midst  of  such  clouds  into  more  definite  knowledge. 
The  formulas  and  the  tables  employed  in  this  paper  are  satis- 
factory, and  it  is  possible  to  accomplish  much  by  using  only 
our  surface  observations.  It  is,  however,  very  important  to 
supplement  such  studies  with  the  actual  observations  in  the 
clouds  by  balloons  and  kites. 


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